rk1_implicit, a MATLAB 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.
Unless the right hand side of the ODE is linear in the dependent variable, each step requires the solution of an implicit nonlinear equation. Such equations can be approximately solved using methods such as fixed point iteration, or an implicit equation solver like fsolve().
The information on this web page is distributed under the MIT license.
rk1_implicit 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.
matlab_ode_solver, a MATLAB code which solves one or more differential equations (ODE) using a method of a particular order, either explicit or implicit. Some methods require a nonlinear equation solver. Some methods used a fixed stepsize, while others adapt the stepsize based on an error estimate.