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Problem 3 Galerkin Method. Using the Galerkin Method, solve the following differential equation with an approximate solution of the form: ũ(x) = c101 + c2$2 = c1x+ c2x². d²u +x² = 0 dx2 0

Problem 3 Galerkin Method. Using the Galerkin Method, solve the following differential equation with an approximate solution of the form: ũ(x) = c101 + c2$2 = c1x+ c2x². d²u +x² = 0 dx2 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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Problem 316 ots Galerkin Method. Using the Galerkin Method, solve the following differential equation with an approximate solution of the form: ü(x) = c1$1+ C2$2 = C1x+ c2x². d?u +x² = 0 dx2 0 <x<1 u(0) = 0 Boundary Conditions:} du (1) = 1 dx Compare your approximate solution with the exact one by plotting them on a -1 4 graph. The exact solution is given by: u(x) =x* +;x. Also, compare the 4 12 3 derivatives du /dx and dũ/dx on a separate plot. What do you observe?
Transcribed Image Text:Problem 316 ots Galerkin Method. Using the Galerkin Method, solve the following differential equation with an approximate solution of the form: ü(x) = c1$1+ C2$2 = C1x+ c2x². d?u +x² = 0 dx2 0 <x<1 u(0) = 0 Boundary Conditions:} du (1) = 1 dx Compare your approximate solution with the exact one by plotting them on a -1 4 graph. The exact solution is given by: u(x) =x* +;x. Also, compare the 4 12 3 derivatives du /dx and dũ/dx on a separate plot. What do you observe?
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