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The following initial-boundary value problem for the heat equation. du =-2 cos p- 5, 0 0 u(0,t) = u(2,1) = 1, t20 u(x,0) = sin 2ax+ cos Tx i. By using finite difference method with step size At = 0.01 and Ar = 0.4 , show that U;r41 =(-0.125 cos p)u,1, +(1+0.25cos p)u;, - (0.125 cos p)u1, 11. Hence, by taking p= n, solve the heat equation above up to t= 0.01.

The following initial-boundary value problem for the heat equation. du =-2 cos p- 5, 0 0 u(0,t) = u(2,1) = 1, t20 u(x,0) = sin 2ax+ cos Tx i. By using finite difference method with step size At = 0.01 and Ar = 0.4 , show that U;r41 =(-0.125 cos p)u,1, +(1+0.25cos p)u;, - (0.125 cos p)u1, 11. Hence, by taking p= n, solve the heat equation above up to t= 0.01.

Advanced Engineering Mathematics
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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2. The following initial-boundary value problem for the heat equation. -2 cos p 0 < x < 2, t > 0 u(0,t) = u(2,1) =1, t20 u(x,0) = sin 2ax + cos TX i. By using finite difference method with step size At = 0.01 and Ar = 0.4, show that Up1 =(-0.125 cos pu,1, +(1+0.25cos p)u,, - (0.125 cos plu1, i-1,t 11. Hence, by taking p = n, solve the heat equation above up to t= 0.01.
Transcribed Image Text:2. The following initial-boundary value problem for the heat equation. -2 cos p 0 < x < 2, t > 0 u(0,t) = u(2,1) =1, t20 u(x,0) = sin 2ax + cos TX i. By using finite difference method with step size At = 0.01 and Ar = 0.4, show that Up1 =(-0.125 cos pu,1, +(1+0.25cos p)u,, - (0.125 cos plu1, i-1,t 11. Hence, by taking p = n, solve the heat equation above up to t= 0.01.
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