Given an initial-boundary value problem for the heat equationu, = 2u, 00u(0,t) = u(2,t) = 0, t>0и(х,0) — 4x(2— х)а)By using finite difference method, show thatu;1 = 0.25u,-1, +0.5u,, +0.25u,with step size At =0.02 and Ax=0.4.b)Then, solve the equation up to t=0.02. (Write the answer in two decimal places.)

Explicit Method: If the initial -boundary value problem is…

Given an initial-boundary value problem for the heat equation u, = 2u , 00 u(0,t) = u(2,t) =0, t20 u(x,0) = 4x(2– x) By using finite difference method, show that u1 = 0.25u,-1, +0.5u,, +0.25,4 with step size At = 0.02 and Ar=0.4. a) i-1,t b) Then, solve the equation up to t = 0.02. (Write the answer in two decimal places.)

Given an initial-boundary value problem for the heat equation u, = 2u , 00 u(0,t) = u(2,t) =0, t20 u(x,0) = 4x(2– x) By using finite difference method, show that u1 = 0.25u,-1, +0.5u,, +0.25,4 with step size At = 0.02 and Ar=0.4. a) i-1,t b) Then, solve the equation up to t = 0.02. (Write the answer in two decimal places.)

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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Differential Equations

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Question

Given an initial-boundary value problem for the heat equation
u, = 2u, 0<x<2, t>0
u(0,t) = u(2,t) = 0, t>0
и(х,0) — 4x(2— х)
а)
By using finite difference method, show that
u;1 = 0.25u,-1, +0.5u,, +0.25u,
with step size At =0.02 and Ax=0.4.
b)
Then, solve the equation up to t=0.02. (Write the answer in two decimal places.)

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