(4) Solve the boundary value problem 0<< 2, 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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Transcribed Image Text:(5) Solve the Neumann boundary value problem
(6) Solve the Neumann boundary value problem
(4) Solve the boundary value problem
0 <I< 2,
0<y<2,
UIz + Uyy =0,
u(0, y) = u(2, y) = 0,
u(x,0) = 1 – x, u(x,2) = x, 0<x < 2.
0<y< 2,
0 < x <T, 0<y<r,
V²u = 0,
U (0, y) = 0, uz (7, y) = 2 cos y,
Uy (x, 0) = 0, uy(x, 7) = 0
0 <x <T.
0 <x < T, 0 < y< n,
Uzz + Uyy = 0,
Uz (0, y) = uz(7, y) = 0,
Uy (T, 0) = cos r,
0 <x < T.
Uy (x, 7) = 0
7) Solve the boundary value problem
0 < x <1, 0<y<1,
0<y<1,
V²u = 0,
%3D
u(0, y) = y(1– y), u(1, y) = 0,
u(x, 0) = sin
0<x < 1.
2), u(x, 1) = 0
Solve the boundary value problem
Vu = 1+ y,
u(0, y) = 0, u(1, y) = 0,
u(x,0) = 0, u(z, 2) = 0
0 << 1, 0< y<2,
0SyS2,
0<x<1.
Solve the boundary value problem
Vu = -2y,
u(0, y) = 0, u(1, y) = 0,
u(x,0) = 0, u(r, 1) = 0
0 <I<1, 0< y < 1,
%3D
0 <x<1.
26
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