Consider the elliptic PDE Uxx + Uyy = (x² + y²) u(x, 0) = 1, u(0, y) = 1, u(x, 1) = ex, u(3, y) = e³y, 0 < x < 3, where ū = 0 < y < 1 0 ≤ x ≤ 3; 0 ≤ y ≤ 1. When we use the finite difference method to approximate the solution with 4x = 1 and 4y =, we will obtain a system of linear equations of the form AU = b, /U₁1) U₂1 U12 U22 Write down explicitly the elements of the matrix A, and the right hand side vector b. (Do not need to solve the system) (Leave all values in exact expressions, using e as needed.)
Consider the elliptic PDE Uxx + Uyy = (x² + y²) u(x, 0) = 1, u(0, y) = 1, u(x, 1) = ex, u(3, y) = e³y, 0 < x < 3, where ū = 0 < y < 1 0 ≤ x ≤ 3; 0 ≤ y ≤ 1. When we use the finite difference method to approximate the solution with 4x = 1 and 4y =, we will obtain a system of linear equations of the form AU = b, /U₁1) U₂1 U12 U22 Write down explicitly the elements of the matrix A, and the right hand side vector b. (Do not need to solve the system) (Leave all values in exact expressions, using e as needed.)
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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Transcribed Image Text:Consider the elliptic PDE
Uxx + Uyy = (x² + y²)
u(x, 0) = 1,
u (0, y) = 1,
u(x, 1) = ex,
u(3, y) = e³y,
where -
=
0 < x < 3,
When we use the finite difference method to approximate the solution with Ax = 1 and Ay=, we will
obtain a system of linear equations of the form
AU = b,
U₁1
0 < y < 1
0 ≤ x ≤ 3;
0 ≤ y ≤ 1.
U21
U12
U22.
Write down explicitly the elements of the matrix A, and the right hand
side vector b. (Do not need to solve the system) (Leave all values in
exact expressions, using e as needed.)
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