euler, a Python code which solves one or more ordinary differential equations (ODE) using an explicit Runge-Kutta method of order 1, usually known as Euler's explicit method.
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rk1 is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave 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_rk1_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.
cauchy_method, a Python code which solves one or more ordinary differential equations (ODE) using the Cauchy method.
euler, a Python code which uses Euler's method to solve an ordinary differential equation (ODE).
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 nonlinear equation.
rk1_implicit, a Python code which solves one or more ordinary differential equations (ODE) using the Runge-Kutta order 1 implicit method, using fsolve() to solve the implicit equation, and using a fixed time step. rk1_implicit() is commonly called the backward Euler method.
rk12, a Python code which solves an ordinary differential equation (ODE) using a Runge-Kutta (RK) method of order 2, estimating the local error with a Runge-Kutta method of order 1.
rk4, a Python code which applies the fourth order Runge-Kutta (RK) algorithm to estimate the solution of an ordinary differential equation (ODE) at the next time step.
rkf45, a Python code which implements the Runge-Kutta-Fehlberg (rkf) solver for the solution of a system of ordinary differential equations (ODE).
theta_method, a Python code which solves one or more ordinary differential equations (ODE) using the theta method.
trapezoidal, a Python code which solves one or more ordinary differential equations (ODE) using the 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 a 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 second order ordinary differential equation (ODE) of the form y''=f(t,y).
