Consider the following PDE: Vu=3(x-y), in 2; where u(x,y)=x+y Where is the region in the unit square, and 2 its boundary with has shown in the figure below. Piz fi P21 [1] Use the finite difference method to reduce this problem to linear system of equations in the unknowns 11, 12, ¹21 hod (?-iterations) with a suitable initial solution to give the approximate
Consider the following PDE: Vu=3(x-y), in 2; where u(x,y)=x+y Where is the region in the unit square, and 2 its boundary with has shown in the figure below. Piz fi P21 [1] Use the finite difference method to reduce this problem to linear system of equations in the unknowns 11, 12, ¹21 hod (?-iterations) with a suitable initial solution to give the approximate
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
![Consider the following PDE: V²u=3(x-y), in 2;
where u(x, y) = x+y on an
Where is the region in the unit square, and a2 its boundary with h= as shown in the figure below.
3
P12
ti
P21
+
[1] Use the finite difference method to reduce this problem to linear system of equations in the
unknowns U11 U12, 21
[2] Apply the Gauss-Seidel method (2-iterations) with a suitable initial solution to give the approximate
solution of this system, and estimate the approximation error of the last iteration only.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18306282-f933-4068-a09a-779164b2089a%2F7c1008b8-4ded-4e0b-90a5-92514db577b5%2F1h9aag_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following PDE: V²u=3(x-y), in 2;
where u(x, y) = x+y on an
Where is the region in the unit square, and a2 its boundary with h= as shown in the figure below.
3
P12
ti
P21
+
[1] Use the finite difference method to reduce this problem to linear system of equations in the
unknowns U11 U12, 21
[2] Apply the Gauss-Seidel method (2-iterations) with a suitable initial solution to give the approximate
solution of this system, and estimate the approximation error of the last iteration only.
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