Numerical methods II. Theoretical questions

1. Deduce difference scheme of 2nd order accuracy to solve two-point one-dimensional boundary value problem. [1] Section 1.2.

2. Describe piecewise linear Galerkin finite element method to solve two-point one-dimensional boundary value problem. [1] Section 1.3.

3. Removed! Describe finite volume method to solve two-point one-dimensional boundary value problem. [1] Section 1.4, the vertex-centered case.

4. Deduce difference scheme of 2nd order accuracy to solve two-dimensional boundary value problem for Poisson equation. [1] Section 4.2.

5. Deduce explicit difference scheme to solve heat equation in 1D case. When the scheme is stable? [1] Section 3.1.2.

6. Deduce implicit difference scheme and Cranck-Nicolson scheme to solve heat equation in 1D case. When these schemes are stable? [1] Section 3.1.1.

7. Deduce explicit difference scheme to solve wave equation in 1D case. When the scheme is stable? [1] Section 3.5.3 (two-level time marching scheme only).

Reference:

[1] V. Ruas, Numerical methods for partial differential equations. Wiley, 2016. Book is available via EBL http://www.tuee.eblib.com/patron/