Use U₁+1,j + Ujj+1 + Uj-1₁j + Ujj-1-4ui, j = 0 to approximate the solution of Laplace's equation at the interior points of the given region. Use symmetry when possible. (Assume U00= u(0, 0).) U11 = 421 = U12 = 422 = eBook u(0, y) = 216y2(1-y), u(1, y) = 0, 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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Use a computer as a computational aid.
Use U₁+1,j + Ui, j+1 + U¡−1, j + Uj, j-1
(Assume 400 = u(0, 0).)
U11 =
421 =
412 =
422 =
eBook
4ui,j = 0 to approximate the solution of Laplace's equation at the interior points of the given region. Use symmetry when possible.
u(0, y) = 216y²(1 −y), u(1, y) = 0, 0 < y < 1
u(x, 0) = 0, u(x, 1) = 0, 0 < x < 1
==
mesh size: h =
Transcribed Image Text:Use a computer as a computational aid. Use U₁+1,j + Ui, j+1 + U¡−1, j + Uj, j-1 (Assume 400 = u(0, 0).) U11 = 421 = 412 = 422 = eBook 4ui,j = 0 to approximate the solution of Laplace's equation at the interior points of the given region. Use symmetry when possible. u(0, y) = 216y²(1 −y), u(1, y) = 0, 0 < y < 1 u(x, 0) = 0, u(x, 1) = 0, 0 < x < 1 == mesh size: h =
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