stiff

stiff introduces an example of a "stiff" differential equation, shows how the Euler method seems to fail on this example, describes the backward Euler method, shows a special approach for linear ODE's, shows how to solve an implicit algebraic equation, and shows how to use this technique to apply the backward Euler method to general ODE's.

The notes:

• stiff.pdf
• stiff.tex

Matlab:

• backward_euler.m, uses n equal steps of the backward Euler method to solve an ODE, using fsolve() to handle the implicit equation.
• euler.m, uses n equal steps of the Euler method, to solve an ODE.
• rk2.m, uses n equal steps of the Runge Kutta 2 method, to solve an ODE.

Images:

• stiff_backward_euler_explicit_25.png
• stiff_euler_25.png
• stiff_rk2_25.png
• stiff_solution.png
• switchback.png