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b) Given the wave equation subject to boundary conditions and initial conditions U(t,0)= 8²U Ət² au Ət a²U əx²¹ U(0, t) = U(2n, t) = 0, t> 0 = 8- 3x, 0≤I

b) Given the wave equation subject to boundary conditions and initial conditions U(t,0)= 8²U Ət² au Ət a²U əx²¹ U(0, t) = U(2n, t) = 0, t> 0 = 8- 3x, 0≤I

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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b) Given the wave equation subject to boundary conditions and initial conditions U(x,0) = au Ət 8²U Ət² U (0, t) = U(2n, t) = 0, t> 0 { a²U მე2 = 8- 3x, 0≤x<T 67-3x, T ≤ x ≤ 2π, (0, t) = 0, 0≤x≤ 2. i. Using finite difference method, show that the wave equation above can be written as Vij+1 = 0.073U₁+1+1.854Uij +0.073Ui-1j - Uij-1, ㅠ where h = Ax = and k = At = 0.1. 3 Based on part (1), sketch a suitable domain to show the mesh points where the numerical solution are calculated up to t = 0.2. Using results in part (i) and (ii), find the numerical solution up to t-0.1.
Transcribed Image Text:b) Given the wave equation subject to boundary conditions and initial conditions U(x,0) = au Ət 8²U Ət² U (0, t) = U(2n, t) = 0, t> 0 { a²U მე2 = 8- 3x, 0≤x<T 67-3x, T ≤ x ≤ 2π, (0, t) = 0, 0≤x≤ 2. i. Using finite difference method, show that the wave equation above can be written as Vij+1 = 0.073U₁+1+1.854Uij +0.073Ui-1j - Uij-1, ㅠ where h = Ax = and k = At = 0.1. 3 Based on part (1), sketch a suitable domain to show the mesh points where the numerical solution are calculated up to t = 0.2. Using results in part (i) and (ii), find the numerical solution up to t-0.1.
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