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Consider the following heat equation 1 U₁ =₁ 16 xx u(0, t) = u(1,t) = 0, u(x,0) = 2 sin 2πx, Use Ax==₁ At = 0.05, and each of the following numerical method to approximate the solution till t = 0.1, also compare your results at t = 0.1 to the actual solution u(x, t) = 2e sin 2πx. 00 t> 0, 0≤x≤ 1. (a) Use the Forward-Difference method to approximate the solution. (b) Use the Backward-Difference method to approximate the solution. (c) Use Crank-Nicolson method to approximate the solution.

Consider the following heat equation 1 U₁ =₁ 16 xx u(0, t) = u(1,t) = 0, u(x,0) = 2 sin 2πx, Use Ax==₁ At = 0.05, and each of the following numerical method to approximate the solution till t = 0.1, also compare your results at t = 0.1 to the actual solution u(x, t) = 2e sin 2πx. 00 t> 0, 0≤x≤ 1. (a) Use the Forward-Difference method to approximate the solution. (b) Use the Backward-Difference method to approximate the solution. (c) Use Crank-Nicolson method to approximate the solution.

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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Consider the following heat equation 1 Ut = •Uxx₂ 16 u(0, t) = u(1, t) = 0, u(x,0) = 2 sin 2πx, Use Ax = At = 0.05, and each of the following numerical method to approximate the solution till t = 0.1, also compare your results at t = 0.1 to the actual solution u(x, t) = 2e + sin 2x. 0<x< 1, t> 0 t> 0, 0 ≤ x ≤ 1. (a) Use the Forward-Difference method to approximate the solution. (b) Use the Backward-Difference method to approximate the solution. (c) Use Crank-Nicolson method to approximate the solution.
Transcribed Image Text:Consider the following heat equation 1 Ut = •Uxx₂ 16 u(0, t) = u(1, t) = 0, u(x,0) = 2 sin 2πx, Use Ax = At = 0.05, and each of the following numerical method to approximate the solution till t = 0.1, also compare your results at t = 0.1 to the actual solution u(x, t) = 2e + sin 2x. 0<x< 1, t> 0 t> 0, 0 ≤ x ≤ 1. (a) Use the Forward-Difference method to approximate the solution. (b) Use the Backward-Difference method to approximate the solution. (c) Use Crank-Nicolson method to approximate the solution.
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