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Q2) a steel plate of dimensions 4 cm x 4 cm and negligible thickness is in steady state conditions. Given the value of u ,y) on boundaries of the square plate, evaluate values of u at internal nodes, which satisfying Laplace's equation: a² u əx² 2² u + = 0 where 0 ≤ x ≤ 4 and 0 ≤ y ≤ 4 əy² B.C. u= 0 at x = 0 and u = 8 + 2y at x = 4 u = x² at y = 0 and u = x² at y = 4; take Ax = Ay = 1

Q2) a steel plate of dimensions 4 cm x 4 cm and negligible thickness is in steady state conditions. Given the value of u ,y) on boundaries of the square plate, evaluate values of u at internal nodes, which satisfying Laplace's equation: a² u əx² 2² u + = 0 where 0 ≤ x ≤ 4 and 0 ≤ y ≤ 4 əy² B.C. u= 0 at x = 0 and u = 8 + 2y at x = 4 u = x² at y = 0 and u = x² at y = 4; take Ax = Ay = 1

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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Q2) a steel plate of dimensions 4 cm x 4 cm and negligible thickness is in steady state conditions. Given the value of u(x ,y) on boundaries of the square plate, evaluate values of u at internal nodes, which satisfying Laplace's equation: 2² u a² u əx² - 0 where 0 ≤ x ≤ 4 and 0 ≤ y ≤4 Əy² B.C. u= 0 at x = 0 and u = 8 + 2y at x = 4 น = x² at y = 0 and u = x² at y = 4; take Ax = Ay = 1 +
Transcribed Image Text:Q2) a steel plate of dimensions 4 cm x 4 cm and negligible thickness is in steady state conditions. Given the value of u(x ,y) on boundaries of the square plate, evaluate values of u at internal nodes, which satisfying Laplace's equation: 2² u a² u əx² - 0 where 0 ≤ x ≤ 4 and 0 ≤ y ≤4 Əy² B.C. u= 0 at x = 0 and u = 8 + 2y at x = 4 น = x² at y = 0 and u = x² at y = 4; take Ax = Ay = 1 +
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