Numerical Analysis-II

Credit Hours: 3+0

Prerequisite(s): Calculus-I, Linear Algebra, Numerical Analysis-I

Objectives of the course:

This course is designed to teach the students about numerical methods and their theoretical bases. The students are expected to know computer programming to be able to write program for each numerical method. Knowledge of calculus and linear algebra would help in learning these methods

Course Contents:

Forward, backward and centered difference formulae, Lagrange interpolation, Newton’s divided difference formula, Interpolation with a cubic spline, Hermite interpolation, least squares approximation. Richardson’s extrapolation, Newton-Cotes formulae, Numerical integration: Rectangular rule, trapezoidal rule, Simpson’s 1/3 and 3/8 rules, Boole’s and Weddle’s rules,  Gaussianquadrature. Difference and Differential Equation: Formulation of difference equations, solution of linear(homogeneous and inhomogeneous) difference equations with constant coefficients. The Euler and modified Euler method, Runge-Kutta methods and predictor-corrector type methods for solving initial value problems along with convergence and instability criteria. Finite difference, collocation and variational method for boundary value problems.

Recommended Books:

1. Gerald C.F. and Wheatley P.O. Applied Numerical Analysis, Pearson Education, Singapore, 2005.

2. Burden R. L. and Faires J. D. Numerical Analysis, latest edition, PWS Pub. Co.

3. Mathews J.H. Numerical Methods for Mathematics, latest Edition, Prentice Hall International.

4. Chapra S. C. and Canale R. P. Numerical Methods for Engineers, 6th edition, McGraw Hill.

5. Sankara K. Numerical Methods for Scientists and Engineers. 2nded. New  Delhi: Prentice Hall, 2005.

ASSESMENT CRITERIA

Mid Term exam: 30 marks

Sessional: 20 marks

Final Term Exam: 50 marks

Total: 100 marks