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MA6459 Numerical Methods Syllabus - NM Syllabus
Solution of algebraic and transcendental equations - Fixed point iteration method – Newton Raphson method- Solution of linear system of equations - Gauss elimination method – Pivoting - Gauss Jordan method – Iterative methods of Gauss Jacobi and Gauss Seidel - Matrix Inversion by Gauss Jordan method - Eigen values of a matrix by Power method.
UNIT II INTERPOLATION AND APPROXIMATION
Interpolation with unequal intervals - Lagrange's interpolation – Newton?s divided difference interpolation – Cubic Splines - Interpolation with equal intervals - Newton?s forward and backward difference formulae.
UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION
Approximation of derivatives using interpolation polynomials - Numerical integration using Trapezoidal, Simpson's 1/3 rule – Romberg?s method - Two point and three point Gaussian quadrature formulae – Evaluation of double integrals by Trapezoidal and Simpson's 1/3 rules.
UNIT IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
Single Step methods - Taylor?s series method - Euler?s method - Modified Euler's method - Fourth order Runge-Kutta method for solving first order equations - Multi step methods - Milne?s and Adams-Bash forth predictor corrector methods for solving first order equations.
UNIT V BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
Finite difference methods for solving two-point linear boundary value problems - Finite difference techniques for the solution of two dimensional Laplace's and Poisson's equations on rectangular domain – One dimensional heat flow equation by explicit and implicit (Crank Nicholson) methods – One dimensional wave equation by explicit method.
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