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. Plots of the solution and timestep history are created.
The information on this web page is distributed under the MIT license.
midpoint_adaptive 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 (implicit) backward Euler method, using fsolve() to solve the implicit equation, and using a fixed time step.
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, and using a fixed time step.
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.
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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), and using a fixed time step.
midpoint, 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 a fixed time step.
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, and using a fixed time step.
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 implicit equation, and using a fixed time step.
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).
rkf45, a Python code which implements the Runge-Kutta-Fehlberg ODE solver.
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 (implicit) trapezoidal method, and using a fixed time step.
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, and using a fixed time step.
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).
