Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 5CR
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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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ISBN:
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