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Problem 2.6. Consider the boundary value problem -u"(x) + u(x) = x, 0

Problem 2.6. Consider the boundary value problem -u"(x) + u(x) = 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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Problem 2.6. Consider the boundary value problem -u"(x) + u(x) = x, 0<x<1, u(0) = u(1) = 0. a. Verify that the exact solution of the problem is given by u(x) = x- sinh r sinh 1 b. Let U(x) be a solution approximation defined by U(x) = Asin x + B sin 2x + C sin 3mx, where A, B, and C are unknown constants. Compute the residual function R(x) = -U"(x) + U(x) - x. c. Use the orthogonality condition R(2) sin nadz = 0, n = 1,2,3, to determine the constants A, B, and C.
Transcribed Image Text:Problem 2.6. Consider the boundary value problem -u"(x) + u(x) = x, 0<x<1, u(0) = u(1) = 0. a. Verify that the exact solution of the problem is given by u(x) = x- sinh r sinh 1 b. Let U(x) be a solution approximation defined by U(x) = Asin x + B sin 2x + C sin 3mx, where A, B, and C are unknown constants. Compute the residual function R(x) = -U"(x) + U(x) - x. c. Use the orthogonality condition R(2) sin nadz = 0, n = 1,2,3, to determine the constants A, B, and C.
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