rk1, a Octave 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.
The information on this web page is distributed under the MIT license.
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 Octave code which solves one or more ordinary differential equations (ODE) using the backward Euler method.
backward_euler_fixed, a Octave 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 Octave 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 Octave code which solves one or more ordinary differential equations (ODE) using the Cauchy method.
euler, a Octave code which uses Euler's method to solve an ordinary differential equation (ODE).
leapfrog, a Octave code which uses the leapfrog method to solve a second order ordinary differential equation (ODE) of the form y''=f(t,y).
midpoint, a Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method.
midpoint_adaptive, a Octave 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 Octave code which solves one or more ordinary differential equations (ODE) using the (explicit) midpoint method, also called the modified Euler method.
midpoint_fixed, a Octave 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.
rk1_implicit, a Octave 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 Octave code which implements Runge-Kutta solvers of orders 1 and 2 for a system of ordinary differential equations (ODE).
rk23, a Octave code which implements Runge-Kutta ODE solvers of orders 2 and 3.
rk34, a Octave code which implements Runge-Kutta ODE solvers of orders 3 and 4.
rk4, a Octave code which applies the fourth order Runge-Kutta (RK) algorithm to estimate the solution of an ordinary differential equation (ODE).
rk45, a Octave code which implements Runge-Kutta ODE solvers of orders 4 and 5.
rkf45, a Octave code which implements the Runge-Kutta-Fehlberg ODE solver.
theta_method, a Octave code which solves one or more ordinary differential equations (ODE) using the theta method.
trapezoidal, a Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method.
trapezoidal_explicit, a Octave code which solves one or more ordinary differential equations (ODE) using the (explicit) trapezoidal method.
trapezoidal_fixed, a Octave 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 Octave 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).