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Numerical solution of ordinary differential equations, both initial and boundary value equations includes quasilinearization, shooting methods, method of adjoints, classification and solution of partial differential equations by the finite difference method,stability and convergence criteria for various schemes, special attention to nonlinear equations with a strong emphasis on the Navier-Stokes equations.

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Generally topics like Numerical Methods for Differential Equations, Matlab Demo, Taylor series methods for solving ODE's, Runge-Kutta methods for solving ODE's, Multistep methods for solving ODE's, Finite Difference Methods for Hyperbolic Equations, Order of Accuracy of FD Schemes, Stability of FD Schemes, Dissipation and Dispersion of FD Schemes, Finite Difference Methods for Parabolic Equations, Finite Difference Methods for Parabolic Equations, Finite Element Methods for Elliptic Equations are considered very complex & an expert help is required in order to solve the assignments based on topics like FEM for Elliptic Equations Inhomogeneous Dirichlet BC's, FEM for Elliptic Equations quadrature, FEM for Elliptic Equations Inhomogeneous Neumann BC's, FEM for Elliptic Equations (2D), Order of Convergence of FE Methods, Weighted Residual Method, Multigrid Method, Numerical Methods for Partial Differential Equations, Finite Difference Discretization of Elliptic Equations, 1D Problem, Finite Difference Discretization of Elliptic Equations.

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