Make a program implementing the algorithm from Exercise 7.23. Set up a series of test cases for checking that one can handle Dirichlet and Neumann boundary conditions as well as a variable diffusion...

Make a program implementing the algorithm from Exercise 7.23. Set up a series of test cases for checking that one can handle Dirichlet and Neumann boundary conditions as well as a variable diffusion coefficient (use the method of manufactured solutions to test the latter feature).

Exercise 7.23

Write extensions in the algorithm from Exercise 7.22 such that a variable diffusion coefficient is allowed.

Exercise 7.22

Modify Algorithm 7.7 such that one can choose between nonhomogeneous Dirichlet or Neumann conditions at the boundary points.