EXERCISE PROBLEMS
  1. Solve y” – x = 0, 0 ≤ x ≤ 1 with the boundary conditions y(x = 0) = 0 y(x = 1) = 0 by using (i) Collocation method; (ii) Least square method, and (iii) Galerkin's method and compare the results.
  2. Solve y” + y + x = 0, 1 ≤ x ≤ 2 with boundary condition y(x = 0) = 0, y(x = 1) = 0 by using (i) Point collocation, (ii) Least square and (iii) Galerkin method.
  3. Solve x2y” – 2xy’ + 2y = 0, 1 ≤ x ≤ 4 with following boundary conditions y(x = 1) = 0, y(x = 4) = 12 by using (i) Point Collocation; (ii) Least square, and (iii) Galerkin's method and compare the results.
  4. Solve x2y” + 6xy’ + 6y = 1/x2, 1 ≤ x ≤ 2 with boundary conditions y(x = 1) = 1, and y(x = 2) = 2. The exact solution is Use (i) Collocation method, (ii) Least square, and (iii) ...

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