Course
PostgraduateSemester
ElectivesSubject Code
AE702Subject Title
Numerical Methods for Scientific ComputingSyllabus
Mathematical review and computer arithmetic – numbers and errors; Nonlinear equations; Direct methods for linear systems; Iterative Methods for Linear Systems; Eigenvalues and Eigenvectors – power method, inverse power method, QR method; Approximation Theory – norms, orthogonaliza- tion, polynomial approximation, piecewise polynomial approximation, trigonometric approximation, rational approximation, wavelet bases; Numerical Differentiation; Numerical Integration- Romberg Integration, Gauss Quadrature, Adaptive Quadrature; Numerical Ordinary Differential Equations – single step and multi-step methods, Runge-Kutta method, predictor corrector method, stiffness, stability, shooting methods; Introduction to parallel programming system architectures, shared and distributed memory programming, performance.
Text Books
Same as Reference
References
1. John, A. T., Scientific Computing- Vol I, II, III, Springer, (2010).
2. Parviz, M., Fundamentals of Engineering Numerical Analysis, Cambridge, (2010).
3. Steven, C. C, Applied Numerical Methods, McGraw Hill, (2012).
4. Walter, G., Martin, J. G., Felix K., Scientific Computing, Springer, (2010).
5. A.S. Ackleh, E.J. Allen, R.B. Hearfott, P. Seshiyer, Modern Numerical Analysis, CRC, (2009).
6. A. Gilat, V. Subramaniam, Numerical Methods for Engineers and Scientists, Wiley, (2014).