cauchy_method, a Python code which solves one or more ordinary differential equations (ODE) using the Cauchy method, and using a fixed time step.
The computer code and data files described and made available on this web page are distributed under the MIT license
cauchy_method 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.
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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.
velocity_verlet, a Python code which uses a version of the velocity Verlet method to solve a secord order ordinary differential equation (ODE) of the form y''=f(t,y).
Solutions using cauchy_fixed():
Solutions using cauchy_fsolve():