backward_euler

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

Unless the right hand side of the ODE is linear in the dependent variable, each backward Euler 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().

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Source Code:

• backward_euler.m, a version of the backward Euler method that solves the backward Euler equation using fsolve() from the MATLAB Optimization toolbox.

• backward_euler_test.m, calls all the tests.
• backward_euler_test.sh, runs all the tests.
• backward_euler_test.txt, the output file.

• predator_prey_deriv.m, returns the right hand side of the predator prey ODE.
• predator_prey_backward_euler_test.m, solves the predator prey ODE using the backward Euler method.
• predator_prey_backward_euler.png, a plot of the solution.

Accurate solution of the stiff ODE requires a very small stepsize, or the use of an implicit method such as the backward Euler method.

• stiff_deriv.m, returns the right hand side of the stiff ODE.
• stiff_exact.m, returns the exact solution of the stiff ODE.
• stiff_backward_euler.png
• stiff_backward_euler_test.m