MA 322 Scientific Computing

Policy of Attendance

Attendance in all lecture and tutorial classes is compulsory. 

Students, who do not meet 75% attendance requirement will not be allowed to write the end semester examination.

For attendance in the classes, attendance sheets will be circulated. 

Each student is expected to sign against his/her name only.

In case, any student is found marking proxy for some other student, an appropriate disciplinary action will be taken on both students involved in the proxy matter.

Random attendance will also be taken.

Syllabus

Errors; Iterative methods for nonlinear equations; Polynomial interpolation, spline interpolations; Numerical integration based on interpolation, quadrature methods, Gaussian quadrature; Initial value problems for ordinary differential equations - Euler method, Runge-Kutta methods, multi-step methods, predictor-corrector method, stability and convergence analysis; Finite difference schemes for partial differential equations - Explicit and implicit schemes; Consistency, stability and convergence; Stability analysis (matrix method and von Neumann method), Lax equivalence theorem; Finite difference schemes for initial and boundary value problems (FTCS, Backward Euler and Crank-Nicolson schemes, ADI methods, Lax Wendroff method, upwind scheme).

Texts: 

1. D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing, 3rd Ed., AMS, 2002.
2. G. D. Smith, Numerical Solutions of Partial Differential Equations, 3rd Ed., Calrendorn Press, 1985.

References:

1. K. E. Atkinson, An Introduction to Numerical Analysis, Wiley, 1989.
2. S. D. Conte and C. de Boor, Elementary Numerical Analysis - An Algorithmic Approach, McGraw-Hill, 1981.
3. R. Mitchell and S. D. F. Griffiths, The Finite Difference Methods in Partial Differential Equations, Wiley, 1980.

  Lecture Timings