Finite Element Methods Only solve questions 2 Question 1: For each of the following differential equations and stated bo

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Finite Element Methods Only Solve Questions 2 Question 1 For Each Of The Following Differential Equations And Stated Bo 1 (35.93 KiB) Viewed 13 times

Finite Element Methods Only solve questions 2 Question 1: For each of the following differential equations and stated boundary conditions, obtain a one-term solution using Galerkin's method of weighted residuals and the specified trial function. In each case, compare the one-term solution to the exact solution d'y +y = 21 dx2 Oss! (O) = 0 y(1) 0 Nicx) = x - x dy OS! +y2 sin d. (O) = 0 Y()=0 b. Ni(x) = sin TX c dy + y2 = 4x OSX S1 dx (0) 0 (1) = 0 Nicx) = x²(1-x) d. dy - y - 2 0 <10 dx Y(0) 0 (10) = 0 N(x)=x(10-x) e. dx dy 3 dx +y OSISI y(O) = 0 (l)=0 NicxXx - 1) - Question 2: For each of the differential equations given in Question 1, use the method of Example 5.4 to determine the trial functions for a two-term approximate solution using Galerkin's method of weighted residuals.