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Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
book

Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition

by Andrei D. Polyanin, Vladimir E. Nazaikinskii
December 2015
Intermediate to advanced content levelIntermediate to advanced
1643 pages
59h 33m
English
Chapman and Hall/CRC
Content preview from Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
1362 LINEAR PARTIAL DIFFERENTIAL EQUATIONS WITH MATHEMATICA
where f
1
(x) = 0, f
2
(x) = sin(4πx), L = 0.5, and c = 1/(4π). By app lying the explicit central finite
difference method, we c onstruct the approximate numeric al solution of the initial-boundary value
problem.
In the explicit central difference method, each second derivative is replaced by a central differ-
ence approximation. The FD scheme for the linear wave equ a tion is
U
i, j+1
= 2(1 r )U
i, j
+ r(U
i+1, j
+U
i1, j
) U
i, j1
,
where r = (ck/h)
2
. In this FD scheme, we have one unknown value U
i, j+1
that depends explicitly
on th e four known values U
i, j
, U
i+1, j
, U
i1, j
, U
i, j1
at the previous ...
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Publisher Resources

ISBN: 9781466581494