Class: 3rd Numerical Methods


Polynomial interpolation


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Numerical Methods new 1

9

Polynomial interpolation, Lagrange’s interpolation polynomial - divided differences Newton’s divided difference interpolation polynomial - error of interpolation

2

10

Finite difference operators - Gregory – Newton forward and backward interpolations - Stirling’s interpolation formula – interpolation with a cubic spline

2

11

Numerical differentiation - differential formulas in the case of equally spaced points

2

12

Numerical integration - trapezoidal and Simpson’s rules - Gaussian integration - errors of integration formulas

2

13

Numerical solution of ordinary differential equations, The Taylor series method - Euler and modified Euler methods

2

14

Runge–Kutta methods (2ndorder and 4th order only)

2

15

Multistep methods - Milne’s predictor - corrector formulas

2

16

Solution of boundary value problems in ordinary differential equations

4

17

Finite difference methods for solving two dimensional Laplace’s equation for a rectangular region

4

18

Finite difference method of solving heat equation and wave equation with given initial and boundary conditions

4

19

Introduction to partial differential equation(PDE)

4

20

Parabolic partial differential equation

4

21

Elliptic partial differential equation- Finite element methods

4


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