16.3 Wave Equation

INTRODUCTION

In this section we approximate a solution of the one-dimensional wave equation using the finite difference method used in the preceding two sections. The one-dimensional wave equation is the prototype hyperbolic partial differential equation.

Difference Equation Replacement

Suppose u(x, t) represents a solution of the one-dimensional wave equation

(1)

Using two central differences,

,

we replace equation (1) ...

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