Use U₁, j = [U₁+1,j + Uj, j+1 + U₁-1,j + Uj,j-1] and Gauss-Seidel iteration to approximate the solution of Laplace's equation at the interior points of a unit square. Use the mesh size h = The boundary conditions are given. (Assume uoo = u(0, 0). Round your answers to four decimal places.) U11 = 421 = U31 = 412 = 422 = 432 = U13 = 423 = 433 = 4 u(0, y) = 0, u(x, 0) = 0, u(1, y) = 120y, 0
Use U₁, j = [U₁+1,j + Uj, j+1 + U₁-1,j + Uj,j-1] and Gauss-Seidel iteration to approximate the solution of Laplace's equation at the interior points of a unit square. Use the mesh size h = The boundary conditions are given. (Assume uoo = u(0, 0). Round your answers to four decimal places.) U11 = 421 = U31 = 412 = 422 = 432 = U13 = 423 = 433 = 4 u(0, y) = 0, u(x, 0) = 0, u(1, y) = 120y, 0
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
![Use Ui, j =
mesh size h =
411 =
421 =
U31
412 =
422
432
413
423 =
433 =
=
[4;+1,j · + Uj, j+1 + U¡−1,j + Uj,j-1] and Gauss-Seidel iteration to approximate the solution of Laplace's equation at the interior points of a unit square. Use the
The boundary conditions are given. (Assume 400 = u(0, 0). Round your answers to four decimal places.)
eBook
4
u(0, y) = 0,
u(x, 0) = 0,
u(1, y) =
u(x, 1) =
X
X
xxxx
120y, 0 <y< 1
120x, 0<x< 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81926eb6-95c9-4142-b031-f5a656f498ba%2Fedfa44ab-24f9-4def-b4f3-b768534abaf3%2F8wo8pre_processed.png&w=3840&q=75)
Transcribed Image Text:Use Ui, j =
mesh size h =
411 =
421 =
U31
412 =
422
432
413
423 =
433 =
=
[4;+1,j · + Uj, j+1 + U¡−1,j + Uj,j-1] and Gauss-Seidel iteration to approximate the solution of Laplace's equation at the interior points of a unit square. Use the
The boundary conditions are given. (Assume 400 = u(0, 0). Round your answers to four decimal places.)
eBook
4
u(0, y) = 0,
u(x, 0) = 0,
u(1, y) =
u(x, 1) =
X
X
xxxx
120y, 0 <y< 1
120x, 0<x< 1
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