Given the boundary value problema*y" – xy' + y = In rwith the conditionsy(1) = 0, y(2) = -2.%3D(a) Using finite difference method, show that the difference equation for the above problem can bewritten as(1+)m+ (-2+)»+ (1-2).. -hYi-1hYi+12.x;Yiwhere h = Ar.(b) Using equation in part (a) and the boundary conditions, obtain a linear system in the formAy = 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

Given, the boundary value problem x2y''-xy'+y=lnx ...(1) with the…

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Given the boundary value problem

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.CR: Chapter 6 Review

Problem 48CR

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Question

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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