Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Please use the Crank-Nicolson Algorithm to solve the problem

Approximate the solution to the following partial differential equation using the Backward-Difference
method.
a²u
0, 0 <x < 2, 0 < t;
du
-
at
и (0, г) — и(2, 1) — 0,
u(x, 0) = sin x, 0<x< 2.
2
Use m = 4, T = 0.1, and N = 2, and compare your results to the actual solution u(x, t) =
e-(7? /4)1 sin x.
Transcribed Image Text:Approximate the solution to the following partial differential equation using the Backward-Difference method. a²u 0, 0 <x < 2, 0 < t; du - at и (0, г) — и(2, 1) — 0, u(x, 0) = sin x, 0<x< 2. 2 Use m = 4, T = 0.1, and N = 2, and compare your results to the actual solution u(x, t) = e-(7? /4)1 sin x.
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