B.Tech Mathematics

 

MA 322                           Scientific Computing                           3-0-2-8

 

Syllabus: Errors; Numerical methods for solving scalar nonlinear equations; Interpolation and approximations, 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. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing, 3rd Edition, AMS, 2002.
  2. D. Smith, Numerical Solutions of Partial Differential Equations, 3rd Edition, Calrendorn Press, 1985.

 

References:

  1. E. Atkinson, An Introduction to Numerical Analysis, Wiley, 1989.
  2. D. Conte and C. de Boor, Elementary Numerical Analysis - An Algorithmic Approach, McGraw-Hill, 1981.
  3. Mitchell and S. D. F. Griffiths, The Finite Difference Methods in Partial Differential Equations, Wiley, 1980.
  4. L. Burden and J. D. Faires, Numerical Analysis, Brooks/Cole, 2001.