SCIENTIFIC COMPUTING

Code: MA227 | L-T-P-C: 3-0-2-8

Errors; Iterative methods for nonlinear equations; Polynomial interpolation, piecewise linear and cubic splines, spline interpolations; Numerical integration by 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 value problems, boundary value problems and free boundary value problems (FTCS, Backward Euler and Crank-Nicolson schemes, ADI methods, Lax Wendroff method, upwind scheme).

Texts:

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. J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 2nd Edition, Texts in Applied Mathematics, Vol. 12, Springer Verlag, 1993.
4. J. D. Hoffman, Numerical Methods for Engineers and Scientists, McGraw-Hill, 1993.
5. R. Mitchell and S. D. F. Griffiths, The Finite Difference Methods in Partial Differential Equations, Wiley, 1980.
6. G. D. Smith, Numerical Solutions of Partial Differential Equations, 3rd Edition, Calrendorn Press, 1985.