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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
1214 BOUNDARY VALUE PROBLEMS. GREENS FUNCTION
By substituting the values set on the charac te ristics (17 .2.5.2) into the g eneral solution w =
ϕ(x at) + ψ(x + at) of the wave equation, we arrive at a system of linear algebraic equations for
ϕ(x) and ψ(x). As a result, the solution of the Goursat problem is obtained in the form
w(x, t) = f
x + at
2
+ g
x at
2
f(0).
The solution pro pagation domain is the parallelogram bounded by the four lines
x at = 0, x + at = 0, x at = 2c, x + at = 2b.
Literature for Section 17.2: P. M. Morse and H. Feshbach (1953, Vol. 2), S. G. Mikhlin (1970), V. S . Vladi-
mirov (1971, 1988), S. J. Farlow (1982),
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Publisher Resources

ISBN: 9781466581494