Scientific Computing

Code: MA2222 | L-T-P-C: 3-0-2-8

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:

• D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing, Third Edition, American Mathematical Society, 2009.
• G. D. Smith, Numerical Solutions of Partial Differential Equations, Third Edition, Clarendon Press, 1986.

 

References:

• K. E. Atkinson, An Introduction to Numerical Analysis, Second Edition, Wiley, 1989.
• S. D. Conte and C. de Boor, Elementary Numerical Analysis - An Algorithmic Approach, McGraw Hill, 1981.
• R. Mitchell and S. D. F. Griffiths, The Finite Difference Methods in Partial Differential Equations, John Wiley, 1980.
• Richard L. Burden, J. Douglas Faires and Annette M. Burden, Numerical Analysis, Tenth Edition, Cengage Learning, 2015.