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 15CR
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please use the Crank-Nicolson Algorithm to solve it

Approximate the solution to the following partial differential equation using the Backward-Difference
method.
1 a?u
= 0,
16 дх2
du
0 < x < 1, 0 < t;
-
at
u(0, t) = u(1,t) = 0, 0 < t, u(x, 0) = 2 sin 27x, 0<x< 1.
0.1, and N
Use m = 3, T = 0.1, and N = 2, and compare your results to the actual solution u(x, t) =
2e-(72/4)f sin 27x.
Transcribed Image Text:Approximate the solution to the following partial differential equation using the Backward-Difference method. 1 a?u = 0, 16 дх2 du 0 < x < 1, 0 < t; - at u(0, t) = u(1,t) = 0, 0 < t, u(x, 0) = 2 sin 27x, 0<x< 1. 0.1, and N Use m = 3, T = 0.1, and N = 2, and compare your results to the actual solution u(x, t) = 2e-(72/4)f sin 27x.
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ISBN:
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Publisher:
Pearson Addison Wesley,