Numerical Methods: Finite difference approach

COURSE LAYOUT

Week 1: Introduction to Numerical methods, Initial and Boundary value problems, Numerical solution of ODE, Picard’s method, Taylor’s series method, Euler’s method, ModifiedEuler’s method, Runge-Kutta method.Week 2 : Introduction of PDE, Classification of PDE: parabolic, elliptic and hyperbolic. Boundary and initial conditions, Taylor series expansion, analysis of truncation error, Finite difference method: FD, BD & CD, Higher order approximation, Order of Approximation, Polynomial fitting, One-sided approximation.Week 3 : Parabolic equation in 2D, Explicit & Crank-Nicolson method, Alternating direction Implicit method (ADI), Elliptic equations, Solution of Poisson equation with Example,Successive over Relaxation (SOR) method, Solution of Elliptic equation by using ADI method, Example.Week 4 : Hyperbolic equations, solution using Explicit method, Stability analysis of Explicit and Implicit scheme, Example, Characteristics of PDE, Solution of Hyperbolic equation by using methods of Characteristics, Hyperbolic equation of first order, Lax-Wendroff’s method, Wendroff’s method, stability analysis of method, Example.