trapezoidal_explicit, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (explicit) trapezoidal method.
The next solution value is estimated using a forward Euler approximation, and then the trapezoidal method is applied.
The computer code and data files described and made available on this web page are distributed under the MIT license
trapezoidal_explicit is available in a MATLAB version.
backward_euler, a MATLAB code which solves one or more ordinary differential equations (ODE) using the backward Euler method.
backward_euler_fixed, a MATLAB 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.
cauchy_method, a MATLAB code which solves one or more ordinary differential equations (ODE) using the Cauchy method.
euler, a MATLAB code which solves one or more ordinary differential equations (ODE) using the forward Euler method.
leapfrog, a MATLAB code which uses the leapfrog method to solve a second order ordinary differential equation (ODE) of the form y''=f(t,y).
midpoint, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method.
midpoint_explicit, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (explicit) midpoint method, also called the modified Euler method.
midpoint_fixed, a MATLAB 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.
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rk23, a MATLAB code which implements Runge-Kutta ODE solvers of orders 2 and 3.
rk34, a MATLAB code which implements Runge-Kutta ODE solvers of orders 3 and 4.
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rk45, a MATLAB code which implements Runge-Kutta ODE solvers of orders 4 and 5.
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trapezoidal, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method, and MATLAB's fsolve() function to handle the implicit equation.
trapezoidal_fixed, a MATLAB 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 MATLAB 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).