- Finite Element Methods Hw 7 Question 1 For Each Of The Following Differential Equations And Stated Boundary Conditions 1 (70.58 KiB) Viewed 15 times
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. dy + y = 2x d.x2 0<x< 1 y(O) = 0 y(1) = 0 N(x) = x(1 – 12) a. b. day + y = 2 sinx 0<x< 1 dx2 y(0) = 0 y(1) = 0 N(x) = sin TTX c. dy + y2 = 4x 0 < x < 1 dx y(0) = 0 y(1) = 0 Ni(x) = x2(1 - x) d. dy dx - y = 2 0<x< 10 y(0) = 0 y(10) = 0 N. (x) = x²(10 - x)2 e. dạy dr2 + y = x 0<x< 1 dx 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.