Answered: Consider a thin plate of length L and…

Consider a thin plate of length L and width W governed by the heat equation Uf = k(uxx + uyy) for u = (x, y, t) uz = k(uxx + uyy), 0 0 u(x, y, 0) = f(x, y), 0

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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Exponents

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Question

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need solve PDE heat equation

Consider a thin plate of length L and width W governed by the heat equation
Uf = k(uxx + Uyy) for u =
(x, y, t)
Uz = k(uxx + Uyy), 0<x< L,
0 < y < W, t > 0
u(x, y, 0) = f(x, y),
0 < x < L,
0 < y<W
L = 1, W = 1, k = 1/10. u(0, y) = 0, u(L, y) = 0, u(x, 0) = 0, u(x, W) = 0. f (x, y) = xy(1 – x)(1 – y).
%3|
1. Find the general solution
u(x, y,t) = En.m Cn,mPn,m(x,y,t) for n,m (x, y, t) a set of product solutions satisfying the boundary
conditions
2. For the given initial condition, find the particular solution for the problem.

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