3. Solve the following Poisson equation problem by the finite differencemethod 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 exactsolution.

The Poisson equation is uxx+uyy=e-xyx2+y2. The conditions are ux, 0=1, ux, 1=e-x, u0, y=1, u1,…

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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Question

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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