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2 Problem Find a formal solution u(x, y, t) to the initial-boundary value problem (the problem of heat flow in a rectangular plate). {0+ 0 },0 0, (0.y.)-(..) -0,00, u(z,0,1)= u(x, W, t)=0, 00, u(z,y,0)=f(z.), 0

2 Problem Find a formal solution u(x, y, t) to the initial-boundary value problem (the problem of heat flow in a rectangular plate). {0+ 0 },0 0, (0.y.)-(..) -0,00, u(z,0,1)= u(x, W, t)=0, 00, u(z,y,0)=f(z.), 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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2 Problem Find a formal solution u(x, y, t) to the initial-boundary value problem (the problem of heat flow in a rectangular plate). Fu 3 {0 ² + 0 }, 0<x< 0<x<L, 0<y<W, t>0, (0.v.)=(.y.t)=0, 0<y<W, t>0, u(z,0,1)= u(x, W,t)=0, 0<x<L, t>0, (z. y,0)=f(x,y), 0<x<L, 0<y<W. Hint. Assume that the solution has the form u(z,y,t) = V(z,y)T(t).
Transcribed Image Text:2 Problem Find a formal solution u(x, y, t) to the initial-boundary value problem (the problem of heat flow in a rectangular plate). Fu 3 {0 ² + 0 }, 0<x< 0<x<L, 0<y<W, t>0, (0.v.)=(.y.t)=0, 0<y<W, t>0, u(z,0,1)= u(x, W,t)=0, 0<x<L, t>0, (z. y,0)=f(x,y), 0<x<L, 0<y<W. Hint. Assume that the solution has the form u(z,y,t) = V(z,y)T(t).
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