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Consider the boundary-value problem -xy" - y' + 3y = 2x, 0≤x≤ 1, y(0) = y(1) = 0 Let x = 0, x₁ = 0.4, x₂ = 0.7, x3 = 1 (h; are different here). Use the Rayleigh-Ritz method with piecewise linear basis ; to solve this BVP. I have computed some Q values for you: Q2,1 = 0.4, Q2,2 = 0.3 Q4,1 = 0.5, Q4,2 = 1.8333, Q4,3 = 5.5 Q5.2 = -0.18 Q6,1 -0.15, Q6,2 = 0.24 Calculate the missing Q values, namely, Q1,1, Q3,i, and Q5,1. Then assemble the linear system to find c₁ and C₂ such that p(x) = C₁₁ + C₂0₂ is an approximated solution to the BVP.

Consider the boundary-value problem -xy" - y' + 3y = 2x, 0≤x≤ 1, y(0) = y(1) = 0 Let x = 0, x₁ = 0.4, x₂ = 0.7, x3 = 1 (h; are different here). Use the Rayleigh-Ritz method with piecewise linear basis ; to solve this BVP. I have computed some Q values for you: Q2,1 = 0.4, Q2,2 = 0.3 Q4,1 = 0.5, Q4,2 = 1.8333, Q4,3 = 5.5 Q5.2 = -0.18 Q6,1 -0.15, Q6,2 = 0.24 Calculate the missing Q values, namely, Q1,1, Q3,i, and Q5,1. Then assemble the linear system to find c₁ and C₂ such that p(x) = C₁₁ + C₂0₂ is an approximated solution to the BVP.

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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Consider the boundary-value problem -xy" - y' + 3y = 2x, 0≤x≤ 1, y(0) = y(1) = 0 Let x₁ = = 0, X1 = 0.4, x₂ = 0.7, x3 = 1 (h¡ are different here). Use the Rayleigh-Ritz method with piecewise linear basis ; to solve this BVP. I have computed some Q values for you: = = 0.3 Q2,1 = 0.4, Q4,1 = 0.5, Q5,2 = -0.18 Q6,1 Q2,2 Q4,2 = 1.8333, = Q4,3 = 5.5 -0.15, Q6,2 = 0.24 Calculate the missing Q values, namely, Q₁,1, Q3,i, and Q5,1. Then assemble the linear system to find c₁ and C₂ such that p(x) = C₁01 + C₂O2 is an approximated solution to the BVP.
Transcribed Image Text:Consider the boundary-value problem -xy" - y' + 3y = 2x, 0≤x≤ 1, y(0) = y(1) = 0 Let x₁ = = 0, X1 = 0.4, x₂ = 0.7, x3 = 1 (h¡ are different here). Use the Rayleigh-Ritz method with piecewise linear basis ; to solve this BVP. I have computed some Q values for you: = = 0.3 Q2,1 = 0.4, Q4,1 = 0.5, Q5,2 = -0.18 Q6,1 Q2,2 Q4,2 = 1.8333, = Q4,3 = 5.5 -0.15, Q6,2 = 0.24 Calculate the missing Q values, namely, Q₁,1, Q3,i, and Q5,1. Then assemble the linear system to find c₁ and C₂ such that p(x) = C₁01 + C₂O2 is an approximated solution to the BVP.
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