Credits: 3 (3-0-0)
Description
Error analysis and stability of algorithms. Nonlinear equations: Newton Raphson method, Muller’s method, criterion for acceptance of a root, system of non-linear equations. Roots of polynomial equations. Linear system of algebraic equations : Gauss elimination method, LU-decomposition method; matrix inversion, iterative methods, ill- conditioned systems. Eigenvalue problems : Jacobi, Given’s and Householder’s methods for symmetric matrices, Rutishauser method for general matrices, Power and inverse power methods. Interpolation and approximation : Newton’s, Lagrange and Hermite interpolating polynomials, cubic splines; least square and minimax approximations.
Numerical differentiation and integration: Newton-Cotes and Gaussian type quadrature methods.
Ordinary Differential Equations : Initial value problems: single step and multistep methods, stability and their convergence. Boundary value problems: Shooting and difference methods.
Partial Differential Equations : Difference methods for solution of parabolic and hyperbolic equations in one and two-space dimensions, stability and their convergence, difference methods for elliptic equations.