3. Solve the following Poisson equation problem by the finite difference method with h = k = 0.1. Plot the approximate solution. Au = e-" (x² + y²), u(х, 0) %3D 1, и(х, 1) %3 е", те [0,1] u(0, у) %3 1, и(1, у) %3 е", ує (0, 1]). (x, y) € (0, 1) × (0, 1) %3D The exact solution is u(x, y) = e-v. Compare with the graph of the exact solution.
3. Solve the following Poisson equation problem by the finite difference method with h = k = 0.1. Plot the approximate solution. Au = e-" (x² + y²), u(х, 0) %3D 1, и(х, 1) %3 е", те [0,1] u(0, у) %3 1, и(1, у) %3 е", ує (0, 1]). (x, y) € (0, 1) × (0, 1) %3D The exact solution is u(x, y) = e-v. Compare with the graph of the exact solution.
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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![3. Solve the following Poisson equation problem by the finite difference
method with h = k = 0.1. Plot the approximate solution.
{
Au = e- (x² + y²),
u(x, 0) = 1, u(x, 1) = e-", x € [0, 1]
u(0, y) = 1, u(1, y) = e¯V, y € [0, 1].
(x, y) E (0, 1) × (0, 1)
The exact solution is u(x, y) = e-rv. Compare with the graph of the exact
solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5415fbff-03a6-47f1-b26c-b8af4f07f5d9%2F8ec23836-e3df-4533-8c1a-7c37579d4629%2Fmf626h8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Solve the following Poisson equation problem by the finite difference
method with h = k = 0.1. Plot the approximate solution.
{
Au = e- (x² + y²),
u(x, 0) = 1, u(x, 1) = e-", x € [0, 1]
u(0, y) = 1, u(1, y) = e¯V, y € [0, 1].
(x, y) E (0, 1) × (0, 1)
The exact solution is u(x, y) = e-rv. Compare with the graph of the exact
solution.
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