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Problem 2.5. We want to find a solution approximation U(x) to −u"(x)=1, 0

Problem 2.5. We want to find a solution approximation U(x) to −u"(x)=1, 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 2.5. We want to find a solution approximation U(x) to -u"(x) = 1, 0<x<1, u(0) = u(1) = 0, using the ansatz U(x) = Asin x + B sin 2x. a. Calculate the exact solution u(x). b. Write down the residual R(x) = −U"(x) — 1 c. Use the orthogonality condition So to determine the constants A and B. d. Plot the error e(x) = u(x) - U(x). R(x) sin лnx dx = 0, n = 1.2.
Transcribed Image Text:Problem 2.5. We want to find a solution approximation U(x) to -u"(x) = 1, 0<x<1, u(0) = u(1) = 0, using the ansatz U(x) = Asin x + B sin 2x. a. Calculate the exact solution u(x). b. Write down the residual R(x) = −U"(x) — 1 c. Use the orthogonality condition So to determine the constants A and B. d. Plot the error e(x) = u(x) - U(x). R(x) sin лnx dx = 0, n = 1.2.
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