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Finite Difference Method

Background for Hyperbolic Equations

Wave Equation

As an example of a hyperbolic partial differential equation, we consider the wave equation

for0 < x < aand0 < t < b,with the boundary conditions

The wave equation models the displacement u of a vibrating elastic string with fixed ends atx=0andx=a.Although analytic solutions to the wave equation can be obtained with Fourier series, we use the problem as a prototype of a hyperbolic
equation.

Program (Finite-Difference Solution for the Wave Equation)

To approximate the solution of the wave equation

over the rectangle
with
,for
,and
,for
.

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