I. Partial differential equations - introduction - Difference methods - Finite difference approximation to derivatives - Difference methods for parabolic PDE - Convergence and stability - Solution Of - Frankel formula - Adambashforth scheme - Grank - Nicholson and Lasonean formula ADI Method.

II. Difference method for hyuperbolic PDE - One space and two Space dimension - First order equations - System of first order equations - Laxwendzoff explicit method -Wendroff implicit approximations - Numerical solutions by the method of characteristics.

III. Difference methods of elliptic PDE - Difference methods for linear boundary value problem - Five point formula - General second order equation - Finite difference in polar coordinates - Analysis of discretization error of five point approximation.

IV. Variation principle - Wegthted residual methods - Least square
Method partition method, Galerkin method, moment method , cellocation method - Ritz method.

Finite elements
Line segments, triangular element, rectangular element, Numerical integration over finite element - Ritz finite element method, Least square finite element method - Assembly of element equation's - application to initial and boundary value problems.

Text Book:
M.K. Jain : Numerical solutions of ordinary & Partial Differential Equations

REFERENCE BOOK :
1. J.N. Reddy : Introduction to Finite Methods
2. Desai and Abel : Finite Element Methods
3. Zuncowitz : Finite Element Methods