MA8491 Numerical Methods Syllabus:

MA8491 Numerical Methods Syllabus – Anna University Regulation 2017

UNIT I Solution Of Equations And Eigenvalue Problems

Solution of algebraic and transcendental equations – Fixed point iteration method – Newton Raphson method – Solution of linear system of equations – Gaus elimination method – Pivoting – Gaus Jordan method – Iterative methods of Gaus Jacobi and Gaus Seidel – Eigenvalues of a matrix by Power method and Jacobi’s method for symmetric matrices.

UNIT II Interpolation And Approximation

Interpolation with unequal intervals – Lagrange’s interpolation – Newton’s divided difference interpolation – Cubic Splines – Difference operators and relations – 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 Gausian 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 – Kuta method for solving first order equations – Multi step methods – Milne’s and Adams – Bash forth predictor corector methods for solving first order equations.

UNIT V Boundary Value Problems In Ordinary And Partial Differential Equations

Finite difference methods for solving second order two – point linear boundary value problems – Finite difference techniques for the solution of two dimensional Laplace’s and Poison’s equations on rectangular domain – One dimensional heat flow equation by explicit and implicit (Crank Nicholson) methods – One dimensional wave equation by explicit method.