# bdf2

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.

### Languages:

bdf2 is available in a MATLAB version and a Python version.

### Related Data and codes:

backward_euler, a Python code which solves one or more ordinary differential equations (ODE) using the (implicit) backward Euler method.

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.

euler, a Python code which solves one or more ordinary differential equations (ODE) using the forward Euler method.

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_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.

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).

trapezoidal, a Python code which solves one or more ordinary differential equations (ODE) using the (implicit) 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.

### Source Code:

Last revised on 29 May 2022.