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5.6 Exercises Problem 5.1. Consider the two-point boundary value problem u(0) = u(1) = 0. -u" = f, 0

5.6 Exercises Problem 5.1. Consider the two-point boundary value problem u(0) = u(1) = 0. -u" = f, 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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5.6 IExercises Problem 5.1. Consider the two-point boundary value problem u(0) = u(1) = 0. -u" = f, 0<x< 1; Let V = {v: |v|| + ||v|| <∞, v(0) = v(1)=0}. a. Use V to derive a variational formulation of (5.6.1). b. Discuss why V is valid as a vector space of test functions. c. Classify whether the following functions are admissible test functions or not: x Ina, e - 1, a(1-x). sin TX, (5.6.1) x²,
Transcribed Image Text:5.6 IExercises Problem 5.1. Consider the two-point boundary value problem u(0) = u(1) = 0. -u" = f, 0<x< 1; Let V = {v: |v|| + ||v|| <∞, v(0) = v(1)=0}. a. Use V to derive a variational formulation of (5.6.1). b. Discuss why V is valid as a vector space of test functions. c. Classify whether the following functions are admissible test functions or not: x Ina, e - 1, a(1-x). sin TX, (5.6.1) x²,
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