デジタル形式で段階的に解決 ありがとう!! SOLVE STEP BY STEP IN DIGITAL FORMAT Solve by finite differences, (first 4 approximations) Find an approximate solution of Laplace's equation ²u = 0 in the rectangle R = {(x, y), 0 ≤ x ≤ 4, 0 ≤ y ≤ 4}, where u(x,y) denotes the temperature at point (x, y) and the boundary conditions are: u(x, 4) = 180 for 0 < x <4, Uy (2,0)=0 for 0 < x < 4, u(0, y) = 80, for 0 ≤ y < 4, u(4, y) = 0 for 0≤ y < 4. It also graphs the analytical solution and the approximation in a single graph.
デジタル形式で段階的に解決 ありがとう!! SOLVE STEP BY STEP IN DIGITAL FORMAT Solve by finite differences, (first 4 approximations) Find an approximate solution of Laplace's equation ²u = 0 in the rectangle R = {(x, y), 0 ≤ x ≤ 4, 0 ≤ y ≤ 4}, where u(x,y) denotes the temperature at point (x, y) and the boundary conditions are: u(x, 4) = 180 for 0 < x <4, Uy (2,0)=0 for 0 < x < 4, u(0, y) = 80, for 0 ≤ y < 4, u(4, y) = 0 for 0≤ y < 4. It also graphs the analytical solution and the approximation in a single graph.
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:デジタル形式で段階的に解決 ありがとう!!
SOLVE STEP BY STEP IN DIGITAL FORMAT
Solve by finite differences, (first 4 approximations)
Find an approximate solution of Laplace's equation ²u
= 0
in the rectangle R = {(x, y), 0 ≤ x ≤ 4, 0 ≤ y ≤ 4}, where u(x,y) denotes
the temperature at point (x, y) and the boundary conditions are:
u(x, 4) = 180
for
0 < x <4,
Uy (2,0)=0
for
0 < x < 4,
u(0, y) = 80,
for
0 ≤ y < 4,
u(4, y) = 0
for
0≤ y < 4.
It also graphs the analytical solution and the approximation in a single graph.
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