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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
22.4. Numerical Solutions and Their Visualizations 1317
Example 22.34. Linear heat equation. Initial-boundary value problem. Num erical, graphi-
cal, and exact solu tions. Crank –Nicolson method. Consider the following initial-boundary value
problem for the linear one-dimensio nal heat equation:
u
t
= k u
xx
, 0 < x < L, t > 0, u(x,0) = f (x), u(0,t) = g
1
(t), u(L,t) = g
2
(t),
where L = 1, k = 0.1, f (x) = x(1 x), g
1
(t) = 0, and g
2
(t) = 0. By co nstructing the numerical and
graphica l solutions of this problem, we apply on e of the suc cessful implicit finite difference schemes
based on six grid points, the
CrankNicholson
method [see Crank and Nicolso n
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Publisher Resources

ISBN: 9781466581494