## Details of ID4104 (Autumn 2018)

 Level: 4 Type: Laboratory Credits: 4.0

Course CodeCourse NameInstructor(s)
ID4104 Numerical Analysis Laboratory Koel Das

Syllabus
Numerical Analysis

Solution of Non-linear Equations: Bisection method, fixed point iteration method, Newton-Raphson, secant, regula-falsi methods.
Solution of Systems of Linear Equations: Gauss elimination method, Thomas algorithm, Gauss-Jacobi and Gauss-Seidel methods.
Solution of Systems of Non- linear equations: Fixed-point method and Newtons method.
Least Square Method: Fitting of linear, exponential, polynomial curves, fitting of curves which are not linear in constants (either directly or after re parametrization).
Interpolation: Newtons forward, backward and divided difference formulae, Lagranges method, Gauss, Stirling and Bessels formulae, Spline interpolation.
Numerical Differentiation: Formulae based on Newtons forward, backward, divided difference, and Lagranges formulas.

Numerical Integration: Trapezoidal rule, Simpsons 1/3rd and 3/8th rules, Weddles rule; quadrature formulas based on Stirlings and Bessels interpolation formulas.

Solution of Differential Equations: Taylors series method, Picards method and Runge-Kutta methods (1st, 2nd and 4th orders) for solving ODEs, Picards method and Runge-Kutta method (4th order) for solving system of ODEs; Predictor-Corrector method due to Milne and Adams-Bashforth-Moulton, finite difference method and shooting method for solving BVPs; solution of parabolic, elliptic and hyperbolic PDEs.

Eigenvalues and Eigenvectors: Power method, Jacobis method, Givens method, Householders method.

References
Suggested Texts/Reference Books:

1. Atkinson, K., Elementary Numerical Analysis (3rd Edition), Wiley, 2006.

2. Conte, S. D. and De Boor, C., Elementary Numerical Analysis : An algorithmic Approach, Tata McGraw- Hill, 2005.

3. Froberg, C. E., Introduction to Numerical Analysis, Addison-Wesley, 1965.

4. Scarborough, J. B., Numerical Mathematical Analysis (6th Edition), Johns Hopkins University Press, 1966.

#### Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Elective
2 IP 3 Not Allowed
3 IP 5 Not Allowed
4 MR 1 Not Allowed
5 MR 3 Not Allowed
6 MS 7 Elective
7 RS 1 Elective
8 RS 2 Not Allowed