Ordinary Differential Equations: Initial value problems - basic theory and application of multistep methods (explicit and implicit), stability analysis - zero stability, absolute stability, relative stability and intervals of stability, eigen value problems, predictor - corrector methods, Runge-Kutta methods, boundary value problems - shooting methods. Partial Differential Equations:
(a) Parabolic Equations: Explicit and implicit finite difference approximations to onedimensional heat equation, Alternating Direction Implicit (ADI) method.
(b) Hyperbolic equations and Characteristics: Numerical integration along a
characteristic, equations, numerical solution by the method of characteristics,
finite difference solution of second order wave equation.
(c) Elliptic equations: finite difference methods in polar coordinates, techniques near curved boundaries, improvement of accuracy direct
and iterative schemes to solve systems, methods to accelerate the convergence.
(d) Convergence, consistancy and stability
- Teacher: sryedida SANYASIRAJU Y V S S