Exercise 7G 1. 2. Given the boundary value problem: y" = e, for 0≤x≤1, with the boundary conditions, y(0) = 0 and y(1) =

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Exercise 7g 1 2 Given The Boundary Value Problem Y E For 0 X 1 With The Boundary Conditions Y 0 0 And Y 1 1 (68.57 KiB) Viewed 25 times

Exercise 7G 1. 2. Given the boundary value problem: y" = e, for 0≤x≤1, with the boundary conditions, y(0) = 0 and y(1) = 0. (a) Derive the system of linear equations (in matrix-form) using finite-difference method for this problem by taking h= Ax = 0.25. (b) Estimate the values of y(x) at x = 0.25, 0.5, and 0.75 by Thomas algorithm method or calculator. Given the boundary-value problem y" = 12 x², for 1≤x≤2, with the boundary conditions, y(1) = 2 and y(2) = 17. (a) Derive the system of linear equations (in matrix-form) using finite-difference method for this problem by taking h = Ax = 0.2. (b) Estimate the values of y(x) at x = 1.2, 1.4, 1.6, and 1.8 by Thomas algorithm. Answers to Exercise 7G 1. (a) -2 1 03₁ (0.067 1 -2 1 3/₂ = 0.080 0 1 -23). 0.110 (b) y(0.25)= -0.118, (0.5)=-0.169, and y(0.75)= -0.139 2.(a) 1 0 0 -2 1 0 1 -2 1 0 y₁ Y₂ - 1.309 0.941 1229 -15.445 1 0 0 (b) y(0.2) = 3.081, y(0.6) = 7.563, and y(0.8) = 11.504 1 - 2 v y(0.4) = 4.851,