Tutorials
Be it blinking fireflies, chirping crickets, beating hearts, firing neurons or just coupled pendula - through the lens of theoretical physics all of them reduce to differential equations.
This page features short introductions to programming as well as examples on how to numerically solve differential equations in Mathematica, Python, C++ and CUDA.
Mathematica
Infinitesimal Introduction to Mathematica
syntax
solving differential equations
visualizing solutions
animating solutions for presentations
Solving and visualizing dynamical systems
Solve nonlinear ODEs
find fixed points and their linear stability
visualize phase space with trajectories, fixed points and phase space flow
Python
Solving and visualizing dynamical systems
Solve nonlinear ODEs
find fixed points
visualize phase space with trajectories and fixed points
C++
hello world
Simple example for basic commands
double pendulum
Solve differential equations for chaotic double pendulum
visualization either with mathematica or gnuplot
CUDA
hello world
Simple example for basic commands
vector addition
Solve differential equations for chaotic double pendulum
visualization either with mathematica or gnuplot
Turing pattern
solve partial differential equations for Turing pattern formation
visualize pattern evolution with mathematica
save as movie
Starcraft II
Forest Fire
Trees are modified to depend on the states of their neighbors. In this way they act as a cellular automaton.
With an appropriate initial condition and accelerated tree growth it is possible to get a spiral wave.
Video of the result is here: