# The Nature of Mathematical Modelling

## 9.1

### Consider the damped wave equation ∂ 2u ∂t2 = v 2 ∂ 2u ∂x2 + γ ∂ ∂t ∂ 2u ∂x2 . (9.52) Take the solution domain to be the interval [0, 1].

### (a) Use the Galerkin method to find an approximating system of differential equations.

### (b) Evaluate the matrix coefficients for linear hat basis functions, using elements with a fixed size of h.

## 9.2