5. Use the Forward-Difference method to approximate the solution to the following parabolic partial differential cquations. du u a. ar- a -0. 0
5. Use the Forward-Difference method to approximate the solution to the following parabolic partial differential cquations. du u a. ar- a -0. 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:5.
Use the Forward-Difference method to approximate the solution to the following parabolic partial
differential equations.
au
= 0, 0<x< 2, 0 < t;
du
a.
at
ar
и(0, г) %3D и (2, )-0, 0<.
u(x, 0) = sin 27.X, OSxS2.
Use h = 0.4 and k = 0.1, and compare your results at i = 0.5 to the actual solution u(x, t) =
sin 27.x. Then use h = 0.4 and k = 0.05, and compare the answers.
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