ADVANCED NUMERICAL ANALYSIS
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.
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.
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.
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.
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.
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