Initial Value Problems (IVP) and existence theorem. Truncation error, deriving finite difference equations – Single step methods for I order IVP- Taylor series method, Euler method, Picard’s method of successive approximation – Runge Kutta Methods. Stability of single step methods – Multi step methods for I order IVP – Predictor-Corrector method, Euler PC method, Milne and Adams Moulton PC method – Stability of multi step methods, root condition – System of first order ODE, higher order IVPs – Linear Boundary Value Problems (BVP), finite difference methods, shooting methods, stability, error and convergence analysis – Non linear BVP, higher order BVP – Classification of PDEs, Finite difference approximations to partial derivatives – Solution of one dimensional heat conduction equation by Explicit and Implicit schemes (Schmidt and Crank Nicolson methods ), stability and convergence criteria – Laplace equation using standard five point formula and diagonal five point formula, Iterative methods for solving the linear systems – Hyperbolic equation, explicit / implicit schemes, method of characteristics. Solution of wave equation – Solution of I order Hyperbolic equation. Von Neumann stability
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