Introduction to Computational Linear Algebra

Chapter 7

Sparse Systems to Solve Poisson

Differential Equations

In this chapter we consider sparse systems of linear equations resulting from

the discretization by finite difference and finite element methods of ordinary

and partial differential equations. Typically, these discretization methods are

illustrated on one-dimensional and two-dimensional Poisson type differential

equations. There are multiple references to these methods, of which we only

cite [4], [17], [34], [39], [66] and [72].

7.1 Poisson Differential Equations

The starting point is a domain Ω ⊂ R

d

, d = 1, 2. For the one-dimensional

case (d = 1), Ω = (0, L), L > 0 and is assumed to be an open-b ...