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Question 1. Let the partial differential equation (PDE) problem Urr + Uyy = x² + y², (x,y) E N = (0, 1) × (0, 1), u (0, y) = y + 1, u (1, y) = y², u (x, 0) = x + 1, u (x, 1) = x², 0 < y< 1, 0

Question 1. Let the partial differential equation (PDE) problem Urr + Uyy = x² + y², (x,y) E N = (0, 1) × (0, 1), u (0, y) = y + 1, u (1, y) = y², u (x, 0) = x + 1, u (x, 1) = x², 0 < y< 1, 0

Advanced Engineering Mathematics
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 1. Let the partial differential equation (PDE) problem Ugr + Uyy = x² + y², (x,y) E N = (0, 1) × (0, 1) , u (0, y) = y + 1, u (1, y) = y², (x,0) = x + 1, и (г, 1) — х?, 0 <y< 1, 0 <y< 1, 0 < x < 1, 0 <x < 1, econd order (PDE) problem. (b) ! | Construct an explicit central difference scheme for the (PDE) with J intervals in each direction (step size Ax Ay = -) and U (xr, Ys) z u (xr, Ys) for r, s = 1, 2, ..., J –1.
Transcribed Image Text:Question 1. Let the partial differential equation (PDE) problem Ugr + Uyy = x² + y², (x,y) E N = (0, 1) × (0, 1) , u (0, y) = y + 1, u (1, y) = y², (x,0) = x + 1, и (г, 1) — х?, 0 <y< 1, 0 <y< 1, 0 < x < 1, 0 <x < 1, econd order (PDE) problem. (b) ! | Construct an explicit central difference scheme for the (PDE) with J intervals in each direction (step size Ax Ay = -) and U (xr, Ys) z u (xr, Ys) for r, s = 1, 2, ..., J –1.
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