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The solution u(r, 0) of the Laplace equation on a circular disk of radius 3 1 8²u r² 20² 1 a, du. -(r) + rər Ər with boundary condition u(3,0) = 0 is given by u(r, 0) = 0 = 2 for 0≤r≤ 3, -T≤0≤T +Σann sin(ne). n=1

The solution u(r, 0) of the Laplace equation on a circular disk of radius 3 1 8²u r² 20² 1 a, du. -(r) + rər Ər with boundary condition u(3,0) = 0 is given by u(r, 0) = 0 = 2 for 0≤r≤ 3, -T≤0≤T +Σann sin(ne). n=1

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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Partial Differential Equation (PDE), Laplace Equation The solution u(r, 0) of the Laplace equation on a circular disk of radius 3 18 rər ər with boundary condition -(rou). 1 8²u r² 20² + u(r, 0) Show Transcribed Text = 0 = = 2 C for 0≤r≤ 3, T ≤0 ≤ T u(3,0) = 0 is given by + Σann sin(ne). n=1 3 C Compute the coefficients an for n = 0, 1, 2, ...
Transcribed Image Text:Partial Differential Equation (PDE), Laplace Equation The solution u(r, 0) of the Laplace equation on a circular disk of radius 3 18 rər ər with boundary condition -(rou). 1 8²u r² 20² + u(r, 0) Show Transcribed Text = 0 = = 2 C for 0≤r≤ 3, T ≤0 ≤ T u(3,0) = 0 is given by + Σann sin(ne). n=1 3 C Compute the coefficients an for n = 0, 1, 2, ...
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