rk45, a Python code which implements Runge-Kutta ODE solvers of orders 4 and 5.
The computer code and data files described and made available on this web page are distributed under the MIT license
rk45 is available in a MATLAB version and an Octave version and a Python version.
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.
euler, a Python code which solves one or more ordinary differential equations (ODEs) using the forward 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 (ODEs) using the (implicit) midpoint method.
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 ODE solvers of orders 1 and 2.
rk23, a Python code which implements Runge-Kutta ODE solvers of orders 2 and 3.
rk34, a Python code which implements Runge-Kutta ODE solvers of orders 3 and 4.
rk4, a Python code which implements a fourth-order Runge-Kutta-Fehlberg ODE solver.
rkf45, a Python code which implements the Runge-Kutta-Fehlberg ODE solver.
test_ode, a Python code which defines some sample ODE's for testing initial value problem solvers;
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.
