rk12, an Octave 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.
The computer code and data files described and made available on this web page are distributed under the MIT license
rk12 is available in a MATLAB version and an Octave version.
backward_euler, an Octave code which solves one or more ordinary differential equations (ODE) using the backward Euler method.
euler, an Octave code which solves one or more ordinary differential equations (ODE) using the forward Euler method.
leapfrog, an Octave code which uses the leapfrog method to solve a second order ordinary differential equation (ODE) of the form y''=f(t,y).
midpoint, an Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method.
midpoint_explicit, an Octave code which solves one or more ordinary differential equations (ODE) using the (explicit) midpoint method, also called the modified Euler method.
midpoint_fixed, an 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.
rk23, an Octave code which implements Runge-Kutta solvers of orders 2 and 3 for a system of ordinary differential equations (ODE).
rk34, an Octave code which implements Runge-Kutta solvers of orders 3 and 4 for a system of ordinary differential equations (ODE).
rk4, an Octave code which implements a fourth-order Runge-Kutta-Fehlberg solver for a system of ordinary differential equations (ODE).
rk45, an Octave code which implements Runge-Kutta solvers of orders 4 and 5 for a system of ordinary differential equations (ODE).
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trapezoidal, an Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method.
trapezoidal_explicit, an Octave code which solves one or more ordinary differential equations (ODE) using the (explicit) trapezoidal method.
trapezoidal_fixed, an 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.