COMPUTATIONAL METHODS OF ORDINARY DIFFERENTIAL EQUATIONS (Optional Paper)
Initial value problem (IVPS) for the system of ordinary differential equation (ODEs) difference equations numerical methods, Local truncation error, Stability analysis, Interval of absolute stability, Convergence and consistency.
Single step method: Taylor series method, Explicit and implicit Runga-Kutta method and their stability and convergence analysis, Extrapolation method, Runga–Kutta method for first order initial value problems, Runga-Kutta method for the second order initial value problems and their stability analysis, Stiff system of differential equation.
Multi-step methods: Explicit and implicit multi-step methods, General linear multi-step method and their convergence analysis, Adams-Moulton method, Adams-Bashforth method, Nystorm- method, Multi-step methods for the second order IVPS.
Boundary value problem (BVP): Two point nonlinear BVPs for second order ordinary differential equation, Shooting method, Finite difference methods, Convergence analysis, Difference scheme based on quadrature formula, Difference scheme for linear eigen value problems, Mixed boundary condition.
Finite element methods: Assemble of element equations, Variational formulation of BVPs and their solutions, Galerikin method, Ritz method, Finite element solution of BVPs.
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