6 3. Consider the boundary value problem: J²u ²u əx² Əy² u(x,0) = 0, + = 0, u(x, 2) = 0, u(0, y) = 0, u(2, y) = sin ny, (a) Is this a Dirichlet problem or a Neumann problem? (b) Solve this problem completely. (c) Consider the boundary value problem Fu Pu + = 0, dy² ər² u(x,0) = 0, u(r. 2) = sin nr. u(0, y) = 0, u(2, y) = sin ny, 0 < x < 2, 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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6
3. Consider the boundary value problem:
J²u
Əy²
u(x,0) = 0,
J²u
əx²
+
= 0,
u(x, 2) = 0,
u(0, y) = 0,
u(2, y) = sin ny,
(a) Is this a Dirichlet problem or a Neumann problem?
(b) Solve this problem completely.
(c) Consider the boundary value problem
Fu Pu
+
dr² dy²
u(x,0) = 0,
u(x, 2) = sinx,
u(0, y) = 0,
u(2,y) = sin #y,
- = 0,
0 < x < 2,
0 < x < 2,
0 < x < 2,
0 < y < 2,
0 <y<2.
0 < x < 2,
0<x<2,
0 < x < 2,
0<y<2,
0<y<2.
0<y <2,
0<y<2,
7
Explain how you would solve this problem if you already know the solution to the problem
in part (a). You may actually write down the solution (with appropriate explanations), or
just carefully explain the procedure.
Transcribed Image Text:6 3. Consider the boundary value problem: J²u Əy² u(x,0) = 0, J²u əx² + = 0, u(x, 2) = 0, u(0, y) = 0, u(2, y) = sin ny, (a) Is this a Dirichlet problem or a Neumann problem? (b) Solve this problem completely. (c) Consider the boundary value problem Fu Pu + dr² dy² u(x,0) = 0, u(x, 2) = sinx, u(0, y) = 0, u(2,y) = sin #y, - = 0, 0 < x < 2, 0 < x < 2, 0 < x < 2, 0 < y < 2, 0 <y<2. 0 < x < 2, 0<x<2, 0 < x < 2, 0<y<2, 0<y<2. 0<y <2, 0<y<2, 7 Explain how you would solve this problem if you already know the solution to the problem in part (a). You may actually write down the solution (with appropriate explanations), or just carefully explain the procedure.
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