Answer Happy

Finite Element Methods HW #7 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. a. day + y = 2x 0<x< 1 d.x2 y(O) = 0 y(1) = 0 N.(x) = x(1-x2) b. OSXS1 dº y + y = 2 sinx d.x2 y(O) = 0 y(1) = 0 N (X) = sin TX dy + y2 = 4x d.x 0<x<! y(O) = 0 y(1) = 0 Ni(x) = x²(1 - x) d. dy - y = 2 0<< 10 dx y(0) = 0 y(10) = 0 N(x) = x(10-x) e dy dir? dy 3 + y = x 0<x< 1 d.x y(O) = 0 y(1) = 0 N.(x) = x(x - 1)2 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.