velocity_verlet, a Python code which uses a version of the velocity Verlet method to solve a second order ordinary differential equation (ODE) of the form y''=f(t,y).
The computer code and data files described and made available on this web page are distributed under the MIT license
velocity_verlet is available in a MATLAB version and a Python version.
backward_euler, a Python code which solves one or more ordinary differential equations (ODE) using the backward Euler method.
backward_euler_fixed, a Python code which solves one or more ordinary differential equations (ODE) using the (implicit) backward Euler method, using a fixed point iteration for the implicit equation.
bdf2, a Python code which solves one or more ordinary differential equations (ODE) using BDF2, the (implicit) backward difference formula of order 2, using fsolve() to solve the implicit equation.
euler, a Python code which solves one or more ordinary differential equations (ODE) using the Euler method.
leapfrog, a Python code which uses the leapfrog method to solve a second order ordinary differential equation (ODE) of the form y''=f(t,y).
midpoint, a Python code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method.
midpoint_adaptive, a Python code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, relying on fsolve() to solve the implicit equation, and using an adaptive timestep.
midpoint_explicit, a Python code which solves one or more ordinary differential equations (ODE) using the (explicit) midpoint method, also called the modified Euler method.
midpoint_fixed, a Python code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, using a simple fixed-point iteration to solve the implicit equation.
rk12, a Python code which implements Runge-Kutta solvers of orders 1 and 2 for a system of ordinary differential equations (ODE).
rk4, a Python code which applies the fourth order Runge-Kutta (RK) algorithm to estimate the solution of an ordinary differential equation (ODE).
rkf45, a Python code which implements the Runge-Kutta-Fehlberg ODE solver.
trapezoidal, a Python code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method.
trapezoidal_explicit, a Python code which solves one or more ordinary differential equations (ODE) using the (explicit) trapezoidal method.
trapezoidal_fixed, a Python code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method, using the fixed point method to handle the implicit system.
