Simulator Library
Math and Numerical Method Simulators
Math simulators for linear algebra, calculus, statistics, probability, numerical methods, and signal processing.
159 simulators
Related topics in this field
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Simulator list
Adaptive Filter Lms Simulator
Signal Processing
Use MSE convergence, estimated filter shape, and stability map to find fast but stable adaptation.
AM/FM Modulation Simulator
Signal Processing
Learn how a message signal such as audio is "carried" by a radio wave through modulation.
Autocorrelation Function Simulator — Period Detection
Signal Processing
Use the biased autocorrelation R_xx[k] to detect the period of a sinusoid buried in noise. Adjust amplitude, frequency, noise and sample count to learn how period estima…
Bayes' Theorem Visualizer — Conditional Probability & Posterior Update
Adjust prior probability, true positive rate, and false positive rate to calculate posterior probability in real time. Intuitively understand probability updating from e…
Bayesian Calibration via MCMC (Metropolis–Hastings) Simulator
Monte Carlo & Uncertainty
Calibrate a CAE model parameter the Bayesian way: feed in a prior, a likelihood and observed data.
Bézier Curve Simulator
An interactive tool for the smooth curves that just a handful of control points can "shape".
Bifurcation Diagram Simulator — Logistic Map and Chaos
Visualize the logistic map's period-doubling route to chaos. Explore bifurcation diagrams and the Feigenbaum constant with this interactive simulator.
Binomial Distribution Simulator
Binomial distribution B(n,p) simulator. Vary trials n and probability p to visualize PMF, CDF and Poisson/normal approximations in real time.
Bisection Method Simulator — Root Finding by Interval Bracketing
Find roots of f(x)=0 with the bisection method on f(x)=x^3-2x-5. Visualize midpoints, the shrinking bracket and log10 width decay. Tune interval, tolerance, max iter.
Bit Error Rate (BER) Simulator
Signal Processing
Compute the bit error rate (BER) that decides the quality of a digital link.
Bootstrap Confidence Interval Simulator
Monte Carlo & Uncertainty
Compute 95% bootstrap confidence intervals for the mean and median in real time. Resample with replacement and vary N and B to watch the distribution converge.
Break-Even Analysis Simulator — Fixed Costs, Variable Costs & Profit
Determine break-even point, profit margin, and margin of safety by adjusting fixed costs, variable cost per unit, and selling price. Interactive cost-volume-profit chart.
Brownian Motion & Random Walk Simulator
Monte Carlo & Uncertainty
Simulate Brownian motion and random walks in real time. Adjust particles, step size, and trails to verify Einstein's diffusion formula and explore parameters.
Buckingham Pi Theorem Simulator — Dimensional Analysis & Model Similitude
Visualize how five variables for cylinder drag collapse into two dimensionless groups (Re and C_D). Link model and prototype through dynamic similitude and learn how sca…
Buffon's Needle Simulator — Estimating Pi by Probability
Monte Carlo & Uncertainty
The classical experiment: drop needles at random on a floor of equally spaced parallel lines and estimate pi from the crossing probability. Change the count, length, spa…
Capacity Planning Little Law Simulator
Use Little’s law and a capacity screen to relate arrival rate, service time, parallel servers, WIP, and utilization.
CFL Number Simulator — Stability of Explicit Time Integration
Real-time Courant number calculator for explicit time integration. Adjust advection speed u, time step dt, grid spacing dx and CFL_max to monitor 1D advection stability.
Chi-Squared Goodness-of-Fit Test Simulator — Pearson's Test
Chi-squared goodness-of-fit test simulator. Vary the four observed counts O_i to compute chi-squared statistic, df, 5% critical value, and the H_0 decision in real time.
Chirp-Z Transform / Zoom-DFT Simulator — High-Resolution Narrow-Band Analysis
Signal Processing
The plain DFT splits 0..F_s/2 into N equal bins. The Chirp-Z transform (CZT) zooms into any range [f_start, f_end] with M bins. Watch two closely spaced tones become res…
Cholesky Decomposition Simulator
Factor a symmetric 3×3 matrix into the product of a lower-triangular matrix and its transpose, A=LLᵀ.
Complex Function & Conformal Mapping Visualizer
Visualize complex functions with domain coloring. Explore conformal mapping, Joukowski transforms, and the residue theorem interactively.
Complex Number Visualizer — Argand Plane, Polar Form & Operations
Manipulate two complex numbers on the complex plane in real time. Explore addition, subtraction, multiplication, division, conjugates, modulus, polar form, De Moivre's t…
Complex Number & Phasor Calculator
Real-time calculation of arithmetic, exponentiation, and square roots in rectangular and polar forms. Draw vectors on the Argand diagram and animate AC circuit impedance…
Compound Interest Simulator
Visualize compound asset growth in real time. Adjust principal, annual rate, contributions and inflation to compare with simple interest and apply the Rule of 72.
Compressive Sensing & L1 Reconstruction Simulator
Signal Processing
A hands-on simulator for compressive sensing: recover a "sparse" N-dimensional signal that has only K non-zero entries from far fewer than Nyquist measurements, using L1…
Matrix Condition Number Simulator
Compute the condition number κ(A) of a 2×2 matrix and visualize its ill-conditioning.
Conic Sections Explorer — Ellipse, Parabola & Hyperbola Visualizer
Interactively adjust parameters for circles, ellipses, parabolas, and hyperbolas in real time. Visualize foci, directrices, eccentricity, polar form, and the corresponde…
Conjugate Gradient Method Simulator — CG vs Steepest Descent
The conjugate gradient simulator iteratively solves Ax=b for a symmetric positive definite matrix and compares the residual history with steepest descent in real time.
Control Variates Simulator
Monte Carlo & Uncertainty
Experience the control variates method, which boosts Monte Carlo accuracy almost for free. Using an auxiliary variable strongly correlated with your target, watch how mu…
Crank Nicolson Simulator
Crank Nicolson Simulator updates live numeric results and charts as inputs change, supporting early design checks and model review.
Derivative & Tangent Line Visualizer
Select a function and move x to see how the tangent line changes
Design of Experiments (DOE) Simulator
Switch between full factorial, fractional factorial, Central Composite Design (CCD) and Plackett-Burman to compare required runs, statistical power and savings vs OFAT i…
DFT Leakage Window Detail Simulator
Signal Processing
DFT Leakage Window Detail Simulator updates live numeric results and charts as inputs change, supporting early design checks and model review.
ODE Phase Plane Analysis Tool
Visualize ODE systems with phase planes, nullclines, and stability analysis. Explore predator-prey and pendulum models with real-time RK4 trajectories.
1D Diffusion Equation Solver
Solve the 1D diffusion equation using Crank-Nicolson method. Gaussian, step, and sine initial conditions with Dirichlet/Neumann/periodic BCs.
Digital Filter Designer (IIR/FIR)
Signal Processing
Design Butterworth, Chebyshev, and FIR filters. Visualize frequency response, coefficients, and test signals in real-time with this advanced digital filter designer tool.
Design of Experiments (DOE)
Optimize designs with factorial & Taguchi L9 DOE. Automatically calculate main effects, ANOVA, F-test, and SN ratios for robust engineering analysis.
Dynamic Time Warping (DTW) Simulator
Signal Processing
An interactive tool for Dynamic Time Warping, the classic algorithm that compares two time series whose speed or phase differ by finding the optimal alignment along a st…
SIR Epidemic Model Simulator — Herd Immunity & Outbreak Dynamics
Interactive simulator to explore herd immunity and outbreak dynamics. Adjust parameters for COVID-19, flu, and measles to see how R₀ and vaccination stop epidemics.
Generalized Extreme Value (GEV) Distribution Simulator
Use the Generalized Extreme Value distribution to compute the "100-year event" and the probability that it is exceeded during a 30-year service life.
Eye Diagram Simulator
Signal Processing
Reproduce the "eye diagram" that shows the quality of a high-speed digital signal at a glance.
FFT Spectrum Analyzer — Time-Domain Signal to Frequency Spectrum
Monte Carlo & Uncertainty
Analyze time-series signals with the Fast Fourier Transform. Tweak window functions, sampling frequency and signal components to feel aliasing and leakage.
FFT Spectrum Analyzer Simulator
Signal Processing
Simulate FFT spectrum analysis with up to 5 sine waves. Explore windowing, spectral leakage, THD, and DFT parameters like frequency resolution in real time.
1D Finite Volume Method Simulator — Steady Diffusion
Solve the 1D steady diffusion equation with the finite volume method (FVM). The domain is split into control-volume cells, a flux budget is written for every cell to ass…
FIR Filter Design Simulator — Window Method
Signal Processing
Design linear-phase FIR low-pass filters by the window method. Impulse, dB magnitude, transition width, stopband attenuation and group delay update live.
Fourier Epicycles Simulator — Draw Any Curve with Rotating Circles
Signal Processing
Draw any closed curve with your mouse — the DFT decomposes it into spinning circles (epicycles). Adjust the number of circles to see how Fourier approximation quality ch…
Fourier Series Visualizer — Rotating Phasors & Wave Synthesis
Signal Processing
Explore Fourier series synthesis: simulate square, triangle, and sawtooth waves with 1-50 harmonics. Watch Gibbs phenomenon and harmonic spectrum evolve in real-time.
Fourier Series Simulator — Waveform Synthesis & Harmonic Spectrum
Signal Processing
Explore Fourier series synthesis: simulate square, triangle, and sawtooth waves with 1-50 harmonics. Watch Gibbs phenomenon and harmonic spectrum evolve in real-time.
Fourier Transform Visualizer — FFT Spectrum Analyzer
Signal Processing
Explore Fourier transforms interactively. Adjust signals, windows and frequencies with sliders to visualize real-time waveform and spectrum changes.
Fractal Tree & Snowflake Generator — Self-Similarity & Fractal Dimension
Explore fractal geometry. Generate self-similar trees, Koch snowflakes, Sierpinski triangles, and Dragon curves by tuning parameters. Discover infinite patterns.
Conway's Game of Life — Cellular Automaton Simulator
Explore the universe of Conway's Game of Life. Draw cells, create patterns, and discover emergent complexity driven by three simple rules.
Game Theory Simulator — Nash Equilibrium, Prisoner's Dilemma & Evolutionary Games
Edit game theory matrices and simulate outcomes. Automatically find Nash equilibria and watch cooperation evolve in real-time.
Gauss Quadrature Simulator
Experience Gauss-Legendre quadrature, the rule the finite element method uses to integrate element stiffness matrices.
Gauss Quadrature Simulator — Convergence of Gauss-Legendre Integration
Visualize the sample points and weights of Gauss-Legendre quadrature. Change the point count, integration interval and integrand to learn why few points give high accura…
Gauss-Seidel Simulator — Iterative Solution of Linear Systems
Gauss-Seidel iteration simulator for Ax=b. Sweep SOR omega from 0.5 to 1.9 to visualize convergence trajectories and log10 residual decay in real time.
Gershgorin Circle Theorem Simulator
The Gershgorin circle theorem lets you bound where the eigenvalues of a matrix must be from its entries alone, without ever computing them. Move the diagonal and off-dia…
Gibbs Sampling Simulator
Monte Carlo & Uncertainty
Draw samples from a bivariate normal distribution with Gibbs sampling, the classic MCMC (Markov chain Monte Carlo) method.
Gini Coefficient Simulator — Income Inequality & Lorenz Curve
Interactively visualize the Gini coefficient and Lorenz curve. Adjust the shape of the income distribution and see changes in inequality in real time.
Goertzel Algorithm Simulator — DTMF Single Frequency Detection
Signal Processing
Detect DTMF tones with the Goertzel algorithm. A second-order IIR filter extracts 8 DFT bins in O(N), ideal for embedded single-tone detection without an FFT.
Hilbert Transform & Analytic Signal — Envelope Detection
Signal Processing
Apply a DFT-based Hilbert transform to an AM signal and extract the instantaneous amplitude, phase and frequency from the analytic signal. Change the carrier frequency a…
Huber Regression Robust Simulator
Explore the Huber M-estimator for robust regression. Move the outlier fraction, magnitude and the tuning constant delta to compare OLS and Huber slope bias, asymptotic r…
Hypothesis Test Calculator (z-test & t-test)
Run interactive z-tests and t-tests. Get real-time p-values, see critical regions on a chart, and calculate effect size instantly.
Bilinear Transform Simulator — Analog to Digital IIR
Signal Processing
Convert an analog first-order lowpass filter H(s)=ωc/(s+ωc) into a digital IIR filter with the bilinear transform. Change the cutoff and sampling frequency to see the II…
IIR Filter Designer — Butterworth Low-Pass Magnitude Response
Signal Processing
Design a Butterworth low-pass filter and visualize its gain |H(jω)| on a Bode plot. Change cutoff f_c, order N, stopband edge f_s and attenuation A_s to study roll-off.
Importance Sampling — Efficient Tail Probability Estimation
Monte Carlo & Uncertainty
Estimate the tail probability P(X>t) of the standard normal in parallel with crude Monte Carlo and importance sampling. Tune the proposal mean and standard deviation and…
Inflation & Purchasing Power Simulator — CPI, Real Value & Time Value
Adjust inflation rate, time period, and initial amount to calculate purchasing power change, real interest rate, and Rule of 72 in real time. Compare with Japan, US, and…
Interpolation Methods Comparison
Compare Lagrange, Newton, cubic spline, PCHIP, and linear interpolation on the same chart. Experience Runge's phenomenon with high-degree polynomials.
Inventory Management EOQ & Reorder Point Calculator
Calculate your optimal order quantity and reorder point with this free EOQ calculator. Visualize cost tradeoffs and inventory patterns.
Isotonic Regression Simulator
An interactive tool for monotone nonparametric regression. Adjust sample size, noise level and constraint direction to see PAV (Pool Adjacent Violators) in action, with …
Jacobi Eigenvalue Method Simulator
Find the eigenvalues of a symmetric 3×3 matrix with the Jacobi method — a sequence of plane rotations.
Jacobi Iteration Simulator — Linear Systems
Solve a 2x2 linear system A·x=b by the Jacobi iterative method.
Kaplan-Meier Survival Analysis Simulator
Estimate a survival curve from censored time-to-event data with the Kaplan-Meier method. Adjust the sample size, true median survival and censoring rate to see the chara…
Lagrange Multiplier Optimization Simulator
A tool that visualizes the Lagrange multiplier method for optimizing an objective function under an equality constraint.
Lambert Conformal Conic (LCC) Projection Simulator
Wrap a cone around the Earth so that it intersects along two standard parallels, then project geodetic points onto the developed plane — the LCC projection.
Laplace Transform Calculator & Visualizer
Signal Processing
Master Laplace transforms with our interactive calculator. Visualize f(t) and F(s), compute partial fractions, and explore pole-zero maps in real time.
Latin Hypercube Sampling — LHS vs Plain Monte Carlo
Monte Carlo & Uncertainty
Side-by-side 2D Latin Hypercube and plain Monte Carlo sampling. See how placing exactly one point per row and column changes the integration accuracy at the same sample …
Linear Algebra Matrix Transformation Visualizer
Visualize 2D matrix transformations in real time. Control a 2x2 matrix, animate rotations, scaling, shear, and see eigenvectors and eigenvalues.
Linear Programming
Learn to solve 2-variable linear programming problems visually. See the feasible region, optimal vertex, and objective lines in real-time with graphical method steps.
Linear Regression Simulator
Visualize least-squares linear regression interactively. Add data points and see how the regression line updates in real time.
Loan Amortization Calculator
Simulate monthly payments, total interest and balance for fixed-rate loans. Adjust principal, rate and term interactively.
Logistic Population Growth Model
Simulate population growth, stabilization and overshoot using the logistic equation. Adjust carrying capacity and growth rate.
Lorenz Attractor Simulator — Butterfly Effect & Chaos
Explore chaos theory with a real-time Lorenz Attractor simulator. Adjust parameters, launch trajectories, and witness the butterfly effect in 3D.
LU Decomposition Simulator — Direct Solver for Ax=b
The LU decomposition simulator factors a 3x3 matrix into L and U and solves Ax=b with forward and back substitution in real time, with partial pivoting.
Mandelbrot Set Explorer
Explore the infinite Mandelbrot set fractal in real time. Zoom, pan, and switch to Julia mode to discover its self-similar geometry.
Markov Chain Simulator — Two-State Stationary Distribution and Mixing Time
Two-state Markov chain simulator. Vary p, q to see the stationary distribution π=(q/(p+q), p/(p+q)), the t-step probability P_1(t), and 99% mixing time t_mix.
Matched Filter Simulator — Pulse Detection in Noise
Signal Processing
Matched filter simulator: detect a known pulse in white noise via convolution. Compute input/output SNR and processing gain in real time, visualize gain = L.
Matrix Operations & Eigenvalue Calculator
Compute matrix operations instantly: addition, multiplication, determinant, inverse, eigenvalues, eigenvectors, and solve linear systems. .
Matrix Transformation Visualizer — Geometric Meaning of Linear Algebra
Visualize 2x2 matrix transformations with animation. See the grid, basis vectors, and shapes change while computing determinant and eigenvalues.
MCMC Metropolis-Hastings Sampler — Acceptance & Autocorrelation
Monte Carlo & Uncertainty
Draw samples from an arbitrary 1D distribution with Metropolis-Hastings MCMC. Tune the proposal variance sigma and watch the trace, histogram, and autocorrelation update…
MFCC Feature Simulator — Mel-Frequency Cepstral Coefficients
Signal Processing
Visualize, stage by stage, how a speech signal is turned into MFCC features through pre-emphasis, a Hamming window, FFT, a mel filter bank, logarithm and DCT — the stand…
Monte Carlo Pi Estimator
Monte Carlo & Uncertainty
Estimate π using random numbers! This Monte Carlo simulation drops points into a square to reveal the value of Pi through probability and error analysis.
Monte Carlo Statistics Simulator — π, Integration, CLT
Monte Carlo & Uncertainty
Explore Monte Carlo methods: estimate π, test the Central Limit Theorem, perform integration, and simulate random processes with this interactive statistics simulator.
Morris Elementary Effects Method Simulator
Monte Carlo & Uncertainty
Run the cheapest global sensitivity method — the Morris Elementary Effects (EE) screening — directly in your browser.
Multigrid Simulator — V-cycle for 1D Poisson
Solve the 1D Poisson equation with a V-cycle multigrid method and watch the residual fall by orders of magnitude faster than Gauss-Seidel alone.
Mutual Information (MI) Estimation Simulator
Signal Processing
An interactive playground for I(X;Y), the information-theoretic measure of dependence that captures both linear and non-linear relations.
Newton-Raphson Simulator — Roots of Nonlinear Equations
Find roots of f(x)=0 with the Newton-Raphson method. Visualize tangent steps and the log10 error curve for f(x)=x^3-2x-5. Tune initial guess, tolerance, and relaxation.
Normal Distribution Calculator & Visualizer
Interactive normal distribution tool. Set μ and σ to visualize PDF/CDF, compute probabilities, Z-scores, and percentiles instantly.
Numerical Integration Methods Comparator (Trapezoidal, Simpson, Gauss)
Compare Trapezoidal, Simpson's, Gauss-Legendre & Romberg integration methods. View error convergence rates and accuracy orders in a detailed log-log chart.
Nyquist Sampling Theorem Simulator — Aliasing of Sampled Signals
Signal Processing
Adjust the signal frequency f, sampling rate f_s, observation duration and bit depth N with sliders, and obtain real-time values of the Nyquist frequency f_s/2, alias fr…
Numerical ODE Solver Comparison
Compare Euler, Heun, RK2, RK4, and RK45 ODE solvers. Visualize accuracy and stability on problems like logistic growth and Van der Pol.
Option Pricing Calculator — Black-Scholes Model & Greeks
Calculate call/put option prices, Greeks, and implied volatility in real time. Visualize payoff diagrams and delta curves with our Black-Scholes calculator.
Parseval's Theorem — Energy Conservation in Time and Frequency
Signal Processing
Verify in real time that the time-domain energy of a discrete signal equals its frequency-domain energy under the DFT, using three signal families: sinusoid, rectangular…
Particle Size Distribution (Rosin-Rammler Analysis)
Analyze particle size with Rosin-Rammler, Log-Normal, or GGS models. Compute d10/d50/d90, cumulative curves, and histograms instantly. Perfect for CAE simulation.
PERT/CPM Network Project Schedule Calculator
Calculate project critical path and on-time probability with this PERT/CPM network scheduler. Automates forward/backward pass for up to 12 activities.
Phase Space Portrait — Nonlinear Dynamics & Chaos Visualizer
Visualize nonlinear dynamics and chaos. Simulate Lorenz, Duffing, Van der Pol systems, explore attractors and limit cycles with this interactive RK4 integrator.
Picard Iteration (Fixed-Point) Simulator
Visualize fixed-point iteration — rewrite an equation as x = g(x) and repeat x_{n+1} = g(x_n). Change the map g(x), the starting value and the step count to watch the co…
Polynomial Chaos Expansion (PCE) Simulator
Monte Carlo & Uncertainty
For a Gaussian input X ~ N(μ, σ²) and the model Y = a₁X + a₂X², this tool builds a Hermite Polynomial Chaos Expansion in real time and reads off the mean, variance and S…
Predator-Prey (Lotka-Volterra) Simulator — Population Dynamics
Explore predator-prey dynamics with an interactive Lotka-Volterra simulator. Adjust key parameters and visualize population oscillations and phase portraits.
Population Pyramid Simulator — Age-Sex Structure & Demographic Transition
Population pyramid simulator. Adjust fertility rate, life expectancy and migration to visualize age structure changes in real time, with aging and dependency ratio.
Power Iteration Simulator — Dominant Eigenvalue by Iteration
The power iteration simulator estimates the dominant eigenvalue and eigenvector of a 3x3 symmetric matrix by iterating v ← Av/||Av|| and reading the Rayleigh quotient.
Predictor-Corrector Method Simulator — Heun's Method
A tool that visualizes Heun's method, the two-stage predictor-corrector integrator for ordinary differential equations.
Birthday Paradox Probability Calculator
Calculate and animate the probability that at least two people share a birthday in a group of n people. Interactively explore this famous probability problem that dramat…
Probability Distributions Calculator — Normal, Poisson, Binomial, Exponential
Interactive probability distributions calculator. Plot PDF/PMF and CDF curves, compute percentiles, mean, and variance in real time.
QR Decomposition Simulator — Gram-Schmidt & Least Squares
Factor a 3x3 matrix A into an orthogonal Q and upper-triangular R using Modified Gram-Schmidt, then solve the least-squares system Rx=Qt b by back substitution.
Quadratic Function Explorer
Explore the graph of y = ax² + bx + c interactively. Drag a, b and c sliders to see vertex, axis of symmetry, discriminant and roots plotted live in three tabs.
Quantile Regression Simulator
Place quantile regression (QR) side by side with ordinary least squares.
Quasi-Monte Carlo Simulator — Sobol Sequence
Monte Carlo & Uncertainty
Integrate numerically with low-discrepancy sequences such as the Sobol and Halton sequences. Change the sample count, sequence type and integrand to watch how determinis…
Queuing Theory Simulator — M/M/1 & M/M/c Queue Analysis
Adjust arrival rate λ, service rate μ, and number of servers c to visualize average wait time, queue length, and probability distribution in real time using the Erlang-C…
2D Random Walk Simulator — MSD & Diffusion Coefficient
Monte Carlo & Uncertainty
Simulate 2D random walks in real time. Visualize diffusion laws with MSD plots and switch between lattice, Gaussian, and Lévy flight modes.
Regression Analysis & Curve Fitting
Interactive regression analysis tool: add data points, choose models, and instantly view R², RMSE, fitted equations, and residuals.
Rejection Sampling Simulator — Monte Carlo Sample Generation
Monte Carlo & Uncertainty
When direct sampling from a target p(x) is hard, cover it with a proposal q(x) and an envelope M*q(x) >= p(x), then accept each candidate with probability p(x)/(M*q(x)).…
Response Surface Methodology (RSM) Simulator
A hands-on simulator for Response Surface Methodology — the workhorse technique for optimizing process conditions and formulations with only a handful of experiments.
Richardson Extrapolation & Order of Accuracy Simulator
From three step sizes and three numerical solutions, get the observed order of accuracy p and the Richardson-extrapolated true value u_ext in real time. Designed for CFD…
Ridge Regression (Tikhonov) Shrinkage Simulator
Change the L2 penalty λ of ridge regression (Tikhonov regularisation) and watch the effective degrees of freedom, coefficient shrinkage, bias-variance decomposition and …
Riemann Sum Numerical Integration Visualizer
Compare five numerical integration methods — left, right, midpoint, trapezoidal, and Simpson's rule — intuitively. Increase partition count n and observe how errors conv…
Runge-Kutta Stability Simulator
Visualize the absolute stability of the numerical integrators used to solve ordinary differential equations (Euler, RK2, RK4).
Runge-Kutta Simulator — RK4 vs Euler Accuracy Comparison
Integrate the ODE dy/dx = -k*y in real time using both classical fourth-order Runge-Kutta (RK4) and the explicit Euler method, then compare against the exact decay y = y…
Secant Method Simulator — Derivative-Free Root Finding
Visualize the secant iteration x_{n+1}=x_n-f(x_n)*(x_n-x_{n-1})/(f(x_n)-f(x_{n-1})) on f(x)=x^3-2x-5. Watch secant lines, the log10 error curve, and tune the two initial…
Shannon Channel Capacity Simulator — Information Theory Limit
Signal Processing
Compute the Shannon-Hartley capacity C = B·log2(1+S/N) in real time from bandwidth, signal and noise power. Inspect SNR, spectral efficiency and the bandwidth needed to …
Shooting Method Simulator
Solve a boundary value problem — one with conditions fixed at both ends of an interval — by the shooting method. Guess the initial slope at the left end, integrate to th…
Digital Filter Frequency Response Design Tool
Signal Processing
Design and visualize Butterworth, Chebyshev & Bessel IIR filter responses in real time. Adjust type, order, and cutoff frequency instantly.
Signal Modulation Simulator
Signal Processing
Visualize AM, FM, and PM modulation in real time. Adjust parameters like carrier frequency and modulation index to see waveforms and spectra.
Signal & Noise SNR Analyzer
Signal Processing
Analyze signal integrity in real time. Add noise types, compute SNR/ENOB, and visualize results with this interactive CAE tool.
Sampling Theorem & Aliasing Visualizer
Signal Processing
Visualize the Nyquist-Shannon sampling theorem interactively. See real-time aliasing when sampling is too slow and understand the Nyquist frequency.
Significant Figures, Rounding & Measurement Uncertainty Calculator
Calculate significant figures, apply rounding rules, and determine measurement uncertainty for addition, subtraction, multiplication, division, and more.
Sobol Sensitivity Indices Simulator
Monte Carlo & Uncertainty
A hands-on global sensitivity analysis tool that decomposes how input uncertainty drives output variance into main effects and interactions.
Successive Over-Relaxation (SOR) Simulator
Solve the 1D Laplace equation with an iterative solver. Change the relaxation factor omega to see how much faster convergence becomes when the Gauss-Seidel update is amp…
Natural Cubic Spline Interpolation Simulator
Build a natural cubic spline through 6 data points in real time. Compare it with linear interpolation and a theoretical curve, and see why a tridiagonal system produces …
Spread Spectrum Processing Gain Simulator
Signal Processing
Design a direct-sequence spread spectrum (DSSS) communication link. Adjust the chip rate and data rate to see the processing gain, occupied bandwidth and jamming margin …
Central Limit Theorem Simulator — Sampling Distribution Visualization
Monte Carlo & Uncertainty
Repeatedly sample from uniform, exponential, bimodal, or skewed distributions. Vary sample size n and observe how sample means converge to a normal distribution regardle…
Normal Distribution Simulator
Adjust mean and standard deviation to explore probabilities
Stratified Sampling Simulator
Monte Carlo & Uncertainty
A tool for experiencing stratified sampling, a way to boost the accuracy of Monte Carlo integration for free. Split the interval [0,1] into strata and draw samples evenl…
Supply & Demand Curve Simulator
Shift demand and supply curves in real time to visualize changes in equilibrium price and quantity. Explore price elasticity, consumer surplus, producer surplus, and dea…
Taylor Series Approximation Visualizer
See how polynomials approximate sin, cos, eˣ, ln(1+x) and more. Adjust expansion point and order to explore convergence radius and approximation error interactively.
Thomas Algorithm (Tridiagonal Solver) Simulator
Experience the Thomas algorithm (TDMA) solving a tridiagonal linear system in O(n). It discretises and solves the 1D Poisson boundary-value problem −u''=f, and lets you …
Topology Optimization Map Viewer — SIMP Density Distribution
Generate virtual terrain from mathematical functions and visualize contour maps, gradient heat maps, and cross-section profiles in real time. Learn marching squares cont…
Traffic Flow Simulator — LWR Model Speed-Density-Flow Diagram
Simulate macroscopic traffic flow using the Lighthill-Whitham-Richards (LWR) model. Explore the fundamental diagram and shock-wave propagation in traffic streams.
Unit Circle Trigonometry Animator
Adjust angle θ to confirm how point P on the unit circle and sin, cos, tan values change in real time. Waveform graph and function comparison tabs help intuitively under…
Truncation Error & Order of Accuracy Visualization Tool
Visualize truncation error and order of accuracy with our . Understand numerical methods through interactive graphs and examples.
Uncertainty Propagation & Monte Carlo Analysis Tool
Calculate measurement uncertainty with our free Monte Carlo analysis tool. Simulate error propagation and analyze results online instantly.
Engineering Unit Converter
Convert CAE units instantly: 16 categories, 100+ units. Highlights critical units (Pa, N, m, kg, s, K) and supports SI & mm-tonne-s systems for Abaqus/LS-DYNA.
2D Vector Addition Simulator
Add up to five vectors and calculate the resultant in real time. Intuitively learn vector composition from three perspectives: origin display, tip-to-tail method, and co…
2D Vector Field Visualizer
Visualize 2D vector fields with arrows and streamlines. Explore field properties like vortex, source, and rotation interactively.
Vector Field & Streamline Visualizer
Visualize 2D vector fields with arrows and streamlines. Explore field properties like vortex, source, and rotation interactively.
Waveform Generator & Synthesizer — RMS, FFT Spectrum, THD Calculator
Signal Processing
Design complex waveforms by combining up to 4 signal components. Instantly analyze key metrics like RMS, THD, and crest factor while visualizing the composite result.
Daubechies-4 Wavelet Simulator — db4 Multiresolution Analysis
Signal Processing
Interactive Daubechies-4 (db4) wavelet simulator: multi-level DWT of 1D signals, thresholding of detail coefficients, and reconstruction MSE. Smoother basis than Haar.
Haar Wavelet Transform Simulator — Multiresolution Analysis and Compression
Signal Processing
Apply the Haar wavelet recursively to a 1D signal and visualize the approximation and detail coefficient pyramid. Learn compression ratio and reconstruction error from t…
Window Function Spectral Comparison — Mainlobe Width and Sidelobe Suppression
Signal Processing
Visualize the spectra of rectangular, Hann, Hamming and Blackman windows. Vary the window length, signal frequency and offset to see the trade-off between spectral leaka…
Z-Transform & Digital Signal System Analyzer
Signal Processing
Visualize and analyze digital filters in real-time. Enter H(z) coefficients to get pole-zero plots, frequency & impulse responses, and stability checks.
How to Use
- Select a numerical method category: linear algebra (Gaussian elimination, LU decomposition), calculus (Newton-Raphson, Simpson's rule), statistics (hypothesis testing, regression), or signal processing (FFT, convolution)
- Input your matrix dimensions, function coefficients, dataset size, or signal parameters using the cat-filter selector to refine problem type
- Execute the simulation and compare computed results against analytical solutions or reference values to validate convergence and error bounds
Worked Example
Newton-Raphson root-finding for f(x) = x^3 - 2x - 5: Starting with x0 = 2.5, tolerance 1e-6, and 6 iterations yields root x = 2.0946 with residual 3.2e-7. For a 4x4 linear system with condition number 45.6, Gaussian elimination with partial pivoting produces relative error 2.1e-14 compared to direct inversion, confirming numerical stability. FFT on 1024-point signal (sampling rate 48 kHz) resolves frequency components at 20.83 Hz intervals with magnitude accuracy within 0.1%.
Practical Notes
- For ill-conditioned matrices (condition number >1e6), use LU decomposition with iterative refinement rather than standard Gaussian elimination to reduce rounding error accumulation
- When validating statistical hypothesis tests, cross-reference p-values against published tables; a two-sample t-test with n1=n2=30 and effect size d=0.8 requires power analysis confirmation
- Signal processing: Apply windowing functions (Hann, Hamming) before FFT to reduce spectral leakage; zero-padding to 2^N improves frequency resolution without altering underlying data
- Benchmark convergence rates: linear methods converge at O(h^2), quadratic at O(h^4); document iteration counts for reproducibility across platforms