Consider the application of the Thomas algorithm to the simple implicit scheme used to solve the one-dimensional heat equation (see Section 7.5). Modify the algorithm for other sets of boundary conditions.

a) Dirichlet conditions on both ends: \(u(0, t)=g_{0}, u(L, t)=g_{1}\)

b) Neumann conditions on both ends: \((\partial u / \partial x)(0, t)=g_{0},(\partial u / \partial x)\) \((L, t)=g_{1}\)