Given the boundary value problem

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Given the boundary value problem
a*y" – xy' + y = In r
with the conditions
y(1) = 0, y(2) = -2.
%3D
(a) Using finite difference method, show that the difference equation for the above problem can be
written as
(1+)m+ (-2+)»+ (1-2).. -
h
Yi-1
h
Yi+1
2.x;
Yi
where h = Ar.
(b) Using equation in part (a) and the boundary conditions, obtain a linear system in the form
Ay = b, where h = 0.2.
(c) Write the Gauss Seidel formula for the above system Ay = b found in part (b).
(DO NOT SOLVE the system)
%3D
Transcribed Image Text:Given the boundary value problem a*y" – xy' + y = In r with the conditions y(1) = 0, y(2) = -2. %3D (a) Using finite difference method, show that the difference equation for the above problem can be written as (1+)m+ (-2+)»+ (1-2).. - h Yi-1 h Yi+1 2.x; Yi where h = Ar. (b) Using equation in part (a) and the boundary conditions, obtain a linear system in the form Ay = b, where h = 0.2. (c) Write the Gauss Seidel formula for the above system Ay = b found in part (b). (DO NOT SOLVE the system) %3D
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