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) by ...
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Difference Equation Replacement
(1)