ODEs & PDEs Simulators

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.

Crank Nicolson Simulator updates live numeric results and charts as inputs change, supporting early design checks and model review.

Visualize ODE systems with phase planes, nullclines, and stability analysis. Explore predator-prey and pendulum models with real-time RK4 trajectories.

Solve the 1D diffusion equation using Crank-Nicolson method. Gaussian, step, and sine initial conditions with Dirichlet/Neumann/periodic BCs.

Compare Euler and RK4 methods for solving ODEs. Visualize accuracy differences O(h), O(h²), O(h⁴) by adjusting step size in this interactive numerical analysis tutorial.

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…

Compare Euler, Heun (RK2), and RK4 ODE solvers. Adjust step size to see global error update in real time. Visualize the accuracy difference: O(h), O(h²), O(h⁴).

Compare Euler, Heun, RK2, RK4, and RK45 ODE solvers. Visualize accuracy and stability on problems like logistic growth and Van der Pol.

A tool that visualizes Heun's method, the two-stage predictor-corrector integrator for ordinary differential equations.

Visualize the absolute stability of the numerical integrators used to solve ordinary differential equations (Euler, RK2, RK4).

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…

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…