implicit

Location: http://people.sc.fsu.edu/~jburkardt/classes/math1090_2020/implicit/implicit.html

implicit describes the implicit ODE solvers known as the backward Euler and midpoint methods, and looks at their performance on a stiff differential equations.

The notes:

• implicit.pdf
• implicit.tex

Matlab:

• stiff_euler_backward.m, uses n equal steps of the backward Euler method to solve the stiff problem.
• stiff_euler_backward_test.m, stiff_euler_backward_test(n) calls stiff_euler_backward(n) and plots the result.
• stiff_euler.m, uses n equal steps of the (forward) Euler method to solve the stiff problem.
• stiff_euler_test.m, stiff_euler_test(n) calls stiff_euler(n) and plots the result.
• stiff_exact.m, y = stiff_exact(t) evaluates the exact solution of the stiff problem.
• stiff_midpoint.m, uses n equal steps of the midpoint method to solve the stiff problem.
• stiff_midpoint_test.m, stiff_midpoint_test(n) calls stiff_midpoint(n) and plots the result.
• stiff_prime.m, dudt = stiff_prime(t,y) evaluates the right hand side of the stiff problem.

Images:

• stiff_euler_backward.png
• stiff_euler.png
• stiff_midpoint.png
• switchback.png