Candidates can get Best Engineering Design Books 2018 also a Top List of Main Study Materials for 2017-2018 entrance exam in India.
by Linda C. Schmidt and George Dieter
- To impart knowledge on numerical methods that will come in handy to solve numerically the problems that arise in engineering and technology. this will also serve as a precursor for future research.
- It helps the students to get familiarized with the numerical methods which are necessary to solve numerically the problems that arise in engineering.
ALGEBRAIC EQUATIONS- Systems of linear equations: Gauss Elimination method, pivoting techniques, Thomas algorithm for tridiagonal system – Jacobi, Gauss Seidel, SOR iteration methods – Systems of nonlinear equations: Fixed point iterations, Newton Method, Eigenvalue problems: power method, inverse power method, Faddeev – Leverrier Method.
ORDINARY DIFFERENTIAL EQUATIONS- Runge Kutta Methods for system of IVPs, numerical stability, Adams-Bashforth multistep method, solution of stiff ODEs, shooting method, BVP: Finite difference method, orthogonal collocation method, orthogonal collocation with finite element method, Galerkin finite element method.
FINITE DIFFERENCE METHOD FOR TIME DEPENDENT PARTIAL DIFFERENTIAL EQUATION- Parabolic equations: explicit and implicit finite difference methods, weighted average approximation – Dirichlet and Neumann conditions – Two dimensional parabolic equations – ADI method; First order hyperbolic equations – method of characteristics, different explicit and implicit methods; numerical stability analysis, method of lines – Wave equation: Explicit scheme-Stability of above schemes.
FINITE DIFFERENCE METHODS FOR ELLIPTIC EQUATIONS- Laplace and Poisson’s equations in a rectangular region: Five point finite difference schemes, Leibmann’s iterative methods, Dirichlet and Neumann conditions – Laplace equation in polar coordinates: finite difference schemes – approximation of derivatives near a curved boundary while using a square mesh.
FINITE ELEMENT METHOD- Partial differential equations – Finite element method – orthogonal collocation method, orthogonal collocation with finite element method, Galerkin finite element method.