NUMERICAL METHODS AND SCIENTIFIC COMPUTATION

Methods for Solving Algebraic and Transcendental Equations :

1.1 Ramanujan

1.2 Bisection

1.3 Regula Falsi

1.4 Secant

1.5 Newton-Raphson

Unit-II

Interpolation and Numerical Integration :

2.1 Lagrange interpolation

2.2 Finite difference operators

2.3 Interpolation formula using Differences

2.3.1 Gregory-Newton Forward Difference Interpolation

2.3.2 Gregory-Newton Backward Difference Interpolation

2.4 Numerical Integration

2.4.1 Newton-Cote’s formulae

2.4.2 Trapezoidal rule

2.3.2 Simpson’s 1/3 Rule

2.4.4 Simpson’s 3/8 Rule

2.4.5 Gauss Integration

Unit-III

Methods to Solve System of Linear Equations :

3.1 Direct method for solving system of linear equations

3.1.1 Gauss elimination

3.1.2 LU decomposition

3.1.3 Cholesky decomposition

3.2 Iterative method

3.2.1 Jacobi

3.2.2 Gauss-Seidel

Unit-IV

Numerical Solution of Ordinary Differential Equations :

4.1 Single step methods

4.1.1 Picard

4.1.2 Taylor’s series

4.1.3 Euler

4.1.4 Runge-Kutta

4.2 Multistep methods

4.2.1 Predictor-corrector

4.2.2 Modified Euler

4.2.3 Milne-Simpson