Consider an explicit Euler scheme on 5 nodes for the following PDE problem:Uų = 64 - uz, u (1, t) = 0, u (5, t) = 0, u(x, 0) = uo(x)Find the minimum number of nodes m (in t) for which this scheme is stable given that a solutionwill be calculated to t = 1:%3Dmin(m)

Stability criteria for Explicit Euler scheme is ∆t≤∆x22αwe have ∆x=1α=64∆t≤1128

onsider an explicit Euler scheme on 5 nodes for the following PDE problem: Uų = 64 · uzz, u (1, t) = 0, u (5, t) = 0, u(x, 0) = uo(z) nd the minimum number of nodes m (in t) for which this scheme is stable given that a soli ll be calculated to t = 1: nin(m)

onsider an explicit Euler scheme on 5 nodes for the following PDE problem: Uų = 64 · uzz, u (1, t) = 0, u (5, t) = 0, u(x, 0) = uo(z) nd the minimum number of nodes m (in t) for which this scheme is stable given that a soli ll be calculated to t = 1: nin(m)

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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Question

Consider an explicit Euler scheme on 5 nodes for the following PDE problem:
Uų = 64 - uz, u (1, t) = 0, u (5, t) = 0, u(x, 0) = uo(x)
Find the minimum number of nodes m (in t) for which this scheme is stable given that a solution
will be calculated to t = 1:
%3D
min(m)

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