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For the following boundary value problem, use the collocation method to determine a solution of the form of a second order polynomial y=a+bx+cx². d'y dx² dy -=x, 0

For the following boundary value problem, use the collocation method to determine a solution of the form of a second order polynomial y=a+bx+cx². d'y dx² dy -=x, 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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For the following boundary value problem, use the collocation method to determine a solution of the form of a second order polynomial y=a+bx+cx². d'y dx² =x, 0<x<1; y(0)=1; dy (1) + y(1) = 0 dx Hint: One approach is to choose a first function that satisfies the non-homogeneous boundary conditions and the rest that just satisfy homogeneous bc's. Another approach would be to just use quadratic y=a+bx+cx² directly, and use the BC's to determine some of the coefficients.
Transcribed Image Text:For the following boundary value problem, use the collocation method to determine a solution of the form of a second order polynomial y=a+bx+cx². d'y dx² =x, 0<x<1; y(0)=1; dy (1) + y(1) = 0 dx Hint: One approach is to choose a first function that satisfies the non-homogeneous boundary conditions and the rest that just satisfy homogeneous bc's. Another approach would be to just use quadratic y=a+bx+cx² directly, and use the BC's to determine some of the coefficients.
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