Let Au + u = x^2 + y for x and y be in (0, 1). u(x, O) = x^2, u(x, 1) = x, u(0, y) = 0, u(1, y) = 1. and discretize (x1, х2, х3) %3D (у1, у2, у3) 3 (0.25, О.5, 0.75). Write down a system of linear equations giving the second order finite difference method for this equation on the grid points (xi , yk ) for i, k = 1, 2, 3.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let Au + u = x^2 + y for x and y be in (0, 1). u(x,
0) = x^2, u(x, 1) = x, u(0, y) = 0, u(1, y) = 1. and
discretize (x1, х2, х3) %3 (у1, у2, у3) %3D (0.25, 0.5,
0.75).
Write down a system of linear equations giving
the second order finite difference method for
this equation on the grid points (xi , yk ) for i, k
= 1, 2, 3.
%3D
Transcribed Image Text:Let Au + u = x^2 + y for x and y be in (0, 1). u(x, 0) = x^2, u(x, 1) = x, u(0, y) = 0, u(1, y) = 1. and discretize (x1, х2, х3) %3 (у1, у2, у3) %3D (0.25, 0.5, 0.75). Write down a system of linear equations giving the second order finite difference method for this equation on the grid points (xi , yk ) for i, k = 1, 2, 3. %3D
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