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Q2: A) Find the varitional form for the problem #2 du ((x)) – x² = c, 0

Q2: A) Find the varitional form for the problem #2 du ((x)) – x² = c, 0

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter4: Polynomials
Section4.6: Multiplying Polynomials
Problem 48WE
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Q2: A) Find the varitional form for the problem #2 du ((x)) – x² = c, 0<x<L, d²u dx²x=L = Mo u(0) d (b² dx² 13 (9) = du dx √x=1 = 0 = x=0 0, B) Formulate the strong problem corresponding to weak form → Sk du Jx v dx + Sp ди до дх дх dx + √ uv dx = fvdx vv € H₁₂(N) Q3: Define the linear functional J: H₁₁(2) → R by (v) = a(v, v) - L(v) ப by greas Let u be the unique weak solution to a(u,v) = L(v) in H(2) and suppose that a(...) is a symmetric bilinear form on H(2) prove that 1- u is minimizer. 2- u is unique. 3- The minimizer J(u) can be rewritten under algebraic form J(u) = u Au-ub, Where A, b are repictively the stiffence matrix and the load vector
Transcribed Image Text:Q2: A) Find the varitional form for the problem #2 du ((x)) – x² = c, 0<x<L, d²u dx²x=L = Mo u(0) d (b² dx² 13 (9) = du dx √x=1 = 0 = x=0 0, B) Formulate the strong problem corresponding to weak form → Sk du Jx v dx + Sp ди до дх дх dx + √ uv dx = fvdx vv € H₁₂(N) Q3: Define the linear functional J: H₁₁(2) → R by (v) = a(v, v) - L(v) ப by greas Let u be the unique weak solution to a(u,v) = L(v) in H(2) and suppose that a(...) is a symmetric bilinear form on H(2) prove that 1- u is minimizer. 2- u is unique. 3- The minimizer J(u) can be rewritten under algebraic form J(u) = u Au-ub, Where A, b are repictively the stiffence matrix and the load vector
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