ADVANCED NUMERICAL ANALYSIS
Paper Code:
MAT143 A
Credits:
4
Contact Hours:
60.00
Max. Marks:
100.00
Unit I:
I
Errors - Errors in Numerical Calculation, Numbers and their accuracy, Errors and their analysis, general error formula, Error in a series approximation, Number representation, Numerical Solutions of integral equations, Fredholm integral equation.
Unit II:
II
Finite difference methods, Chedyshev series method, Method using generalized quadrature, Method for degenerate kernels. Numerical solution of ordinary differential equation - two point BVPs, differential methods - second order.
Unit III:
III
Numerov fourth order methods, linear ordinary differential equations, Non- uniform grid methods for the second order BVP. Numerical solution of partial differential equations: classification of partial differential equations. Finite difference approximations to derivatives.
Unit IV:
IV
Laplace's equation: Five- point formula , diagonal five point formula, Jacobi's method, gauss- sedial method and successive over relaxation methods. Parabolic equation in one space dimension. Two levels and three levels difference method - Schmidt method. Laasonen method, Crank Nicolson method, Dufort and Frankel Method. Hyperbolic equation in one space dimension. Explicit three level difference scheme, Implicit scheme, First order hyperbolic equation Lax- Wendroff formula.
Unit V:
V
Finite element methods - introduction, Weighted residual methods, Variation methods, Rayleigh - Ritz method, Grlerkin method, finite elements, Assembly of elements equation. Application of finite element method, One- dimensional and two dimensional problems.
Essential Readings:
- G. M. Philips, P. J. Taylor, Theory and Applications of Numerical Analysis, Academic Press, 1996.
- A. Gourdin, M. Boumhrat, Applied Numerical Methods, Prentice Hall India, New Delhi, 2000.
- S. K.Gupta, Numerical Methods for Engineers, Wiley Eastern, New Delhi, 1995.
- J.W. Thomas, Introduction to Numerical Methods for Partial Differential Equations, Springer, 1999.
- Zhangxin Chen, Finite element methods and their applications, Springer, 1998.
- L. R. Scott. Numerical Analysis, Princeton University Press, 2011.
- S. R. K. Iyengar, R. K. Jain, Mahinder Kumar Jain, Numerical Methods for Scientific and Engineering Computation, New Age International Publishers, 2012.
Academic Year:
