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Comp 327: Applied Numerical Methods Question Paper

Comp 327: Applied Numerical Methods

Course:Bachelor Of Education Science

Institution: Kabarak University question papers

Exam Year:2010

INSTRUCTIONS:
1. This question paper has FOUR questions
2. QUESTION ONE IS COMPULSORY AND HAS 30 MARKS
3. Answer any other TWO questions worth 20 marks each.

QUESTION ONE (30 marks)
(a) Write an algorithm and subsequently a program to solve a quadratic equation (6mks)
(b) What is the use of tolerance value in computing a problem iteratively (2mks)
(c) State the three steps of determining the eigenvalues and eigenvectors (3mks)
(d) What is an error? Explain two sources of error with examples (5mks)
(e) List three direct methods of solving simultaneous linear algebraic equation (3mks)
(f) Explain transpose of matrix with example (2mks)
(g) Write an algorithm for solving a problem in Gauss Jordan method (5mks)
(h) Define following terms giving examples in each
(i) Relative Error
(ii) Absolute error (4mks)

QUESTION TWO (20 marks)
(a) Write a program to solve root of a number using Newton Raphson method (6mks)
(b) List any two Closed Newton-Cotes Quadrature Formulas (2mks)
(c) Determine the types of solutions of the following quadratic equations
(i) 8x2
-8x+2=0
(ii) 8x2
-12x+4=0
(iii) 16x2
+4x+8=0 (6mks)
(d) Define dominant eigenvalues and dominant eigenvectors (2mks)
(e) Write an algorithm for Euler’s method (4mks)

QUESTION THREE (20 marks)
(a) Find the positive roots of the equation x
2
-3=0 using bisection method. Carry out four
iterations (5mks)
(b) What is a characteristic equation in eigenvalues? Write a formula and an algorithm for
finding eigenvalues using power method (6mks)
(c) How do you set convergence criterion of Gauss Seidel Method (2mks)
(d) Explain the initial and boundary condition in ordinary differential equation (4mks)

(e) Determine the coefficient matrix, augmented matrix and solution matrix using example of
three equations of three unknowns (3mks)

QUESTION FOUR (20 marks)
(a) What is the meaning of nonlinear algebraic equation? (2mks)
(b) Write an algorithm to implement Gauss Seidel Method (5mks)
(c) Find the derivative of the following 3x5
- 4x4
+5x-8=0 (2mks)
(f) Derive the sigma notation of Taylor series (3mks)
(g) Write a program to solve 1/1 – x using Simpson’s 1/3 rule. (6mks)
(h) Explain the difference between ordinary differential equation and partial differential
equation (2mks)

Comp 327: Applied Numerical Methods Question Paper

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