Assignment 1:
Assignment 2:
Assignment 3:
Assignment 4:
Q1. Numerical Differentiation: Exercise Set
4.1: 1a, 20.
Q2. (Excise Set 4.3: 2a, 6a,10a) Elements of Numerical Integration: Approximate the following integrals using the Trapezoidal, Simpson’s and Midpoint rules.
Q3 (Exercise Set 4.4: 2a, 4a, 6a) Composite Numerical Integration: Use Composite Trapezoidal, Simpson’s and Midpoint rules to approximate the integral
n=4
Q4. (Exercise Set 4.7: 1a) Gaussian Quadrature
Approximate the following integral using Gaussian quadrature with n=3.
Assignment 5:
Q1. (Exercise Set 5.2: 2c and 4c) Euler’s
Method: Given the initial-value problem
,
with the exact solution .
Use Euler’s method with h=0.25 to approximate the solution, and compare your computed solution with the exact solution at each step.
Assignment 6:
Q1: (Exercise Set 6.1: 6d) Use Gaussian Elimination with Backward
Substitution method (Algorithm 6.1) to solve the following linear system, if
possible, and determine whether row interchanges are necessary.
x1 +x2 +x4 = 2,
2x1 +x2 -x3 +x4 = 1,
-x1 +2x2 +3x3 -x4 = 4,
3x1 -x2 -x3 +2x4 =-3.
Q2: (Exercise Set 6.2: 2c,4c) Find the row interchanges that are required to solve the following linear system using (a) Algorithm 61: Gaussian Elimination with Backward Substitution; (b) Algorithm 6.2: Gaussian Elimination with Partial Pivoting.
5x1 +x2 -6x3 = 7,
2x1 +x2 -x3 = 8,
6x1 +12x2 +x3 = 9.
Q3: (Exercise Set 6.5: 2a) Solve the following linear system using matrix factorization technique.
Q4: (Exercise Set 6.5: 6a): Factor the matrices into LU decomposition using the LU Factorization Algorithm with lii=1 for all i.
Assignment 7:
Q1: (Exercise Set 7.3: 2c,4c) Find the first two iterations using (a) Jacobi method and (b) Gauss-Seidel method for the following linear system, using x(0)=0
4x1 +x2 -x3 +x4 = -2,
x1 +4x2 -x3 -x4 = -1,
-x1 -x2 +5x3 +x4 = 0,
x1 -x2 +x3 +3x4 =-1.
Q2: (Exercise Set 7.3: 9a) Find the first two iterations of the SOR method with for the linear system, using x(0)=0
3x1 -x2 +x3 = 1,
3x1 +6x2 +2x3 = 0,
3x1 +3x2 +7x3 = 0.
Last Revised: 30/8/2004