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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Deborah Hughes-Hallett, Patti Frazer Lock, Andrew M. Gleason, Daniel E. Flath, David Lovelock, Douglas Quinney, Eric Connally, Guadalupe I. Lonzano, Karen R. Rhea, Selin Kalaycýoðlu, William G. McCallum, Adam H. Speigler, Brigitte Lahme, Brad G. Osgood
Difference Equation Replacement
(1)