Subject Code: MA7L001 Subject Name:  Numerical Solution of Ordinary and Partial Differential Equations L-T-P: 3-1-0 Credit:4
Pre-requisite(s):  Ordinary and Partial Differential Equations (MA5L009, MA5L015)
Errors: Round-off error, Truncation error, Absolute error, Relative error, Percentage error; Ordinary Differential equations (ODE): Solutions of Initial Value Problems by Taylor Series, Euler, Improved Euler, Modified Euler, Runge-Kutta methods for First and second order differential equations, Multistep methods (Milne and Adams Bashforth). Consistency, stability and convergence aspects of the methods of IVP.   Boundary Value Problems: Shooting and finite difference methods. Partial Differential Equations (PDE): Classification of PDEs, Finite difference approximations to partial derivatives, Numerical solutions of Elliptic, Parabolic and Hyperbolic partial differential equations. Solutions of Laplace equation by Leibmann’s iteration procedure, Poisson equation, Explicit, Crank-Nickolson, Du Fort Frankel methods for Parabolic PDE. Explicit formula for Hyperbolic PDE and Consistency, stability and convergence aspects of these methods.
Text Books:
  1. Smith G. D. Numerical Solutions to Partial Differential Equations, Oxford University Press
  2. Jain M.K., and  Iyengar S.R.K. Numerical methods for scientific and engineering computation
Reference Books:
  1. Lapidus L. and Pinder G. F. Numerical Solution of Partial Differential Equations in Science and Engineering, John Wiley
  2. Jain M.K. Numerical Solutions of Differential Equations
  3. Smith, Numerical solutions of partial Differential Equations (Finite difference methods)