heat_implicit

Location: http://people.sc.fsu.edu/~jburkardt/classes/math1091_2020/heat_implicit/heat_implicit.html

heat_implicit, shows how an implicit ODE scheme, such as the backward Euler method, can be used to approximate the solution of a time dependent heat equation.

The notes:

• heat_implicit.pdf
• heat_implicit.tex

Exercises: Look at these after you have tried to do the work on your own.

• exercise1.m, solve a heat equation using the backward Euler method, with a Neumann boundary condition.
• exercise1.png, a snapshot of the exact and approximate solutions at step 4.
• exercise2.m, repeat exercise1, but use a symmetry boundary condition.
• exercise3.m, repeat exercise 1, using the Crank Nicolson method
• exercise4.m, repeat exercise 2, using the Crank Nicolson method.

Homework: My version posted after you have turned yours in.

• hw4.m, create a theta_method code.
• hw4.png, plot of the computed and exact solutions for time step 10, using hw4(0.0), the forward Euler method.

Images:

• relue.png, a picture of backward Euler.
• stiff_euler.png, approximating a stiff equation with the Euler method.
• stiff_euler_backward.png, approximating a stiff equation with the backward Euler method.