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NUMERICAL METHODS LECTURE NOTES VERY EASY TO UNDERSTAND
Rajan Sharma

NUMERICAL METHODS LECTURE NOTES VERY EASY TO UNDERSTAND

Rajan Sharma | 08-Jan-2016 |
SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS , Solution of equation , Fixed point iteration , Newton’s method , Gauss – Jacobi method , Solution of linear system by Gaussian elimination , Gauss – Jordon method , Gauss – Seidel method , Inverse of a matrix by Gauss Jordon method , Eigenvalue of a matrix by power method , Jacobi method for symmetric matrix , INTERPOLATION AND APPROXIMATION , Lagrangian Polynomials , Divided differences , Interpolating with a cubic spline , Newton’s forward difference formula , Newton’s backward difference formula , Differentiation using interpolation formulae , Numerical integration by trapezoidal rule , Simpson’s 1/3 and 3/8 rules Romberg’s method , Two and Three point Gaussian quadrature formulas , Double integrals using trapezoidal and simpsons’s rules , Taylor series method , Euler methods , Runge-Kutta method for solving first and second order equations , Milne’spredictor and corrector method , Adam’s predictor and corrector method , Finite difference solution of second order ordinary differential equation , Finite difference solution of one dimensional heat equation by explicit and implicit methods , One dimensional wave equation , Two dimensional Laplace equation , Poisson equation ,

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UNIT I

SOLUTION OF EQUATIONS AND

EIGENVALUE PROBLEMS

Solution of equation

Fixed point iteration: x=g(x) method

Newton’s method

Solution of linear system by Gaussian elimination

Gauss – Jordon method

Gauss – Jacobi method

Gauss – Seidel method

Inverse of a matrix by Gauss Jordon method

Eigenvalue of a matrix by power method

Jacobi method for symmetric matrix.

 

UNIT II

INTERPOLATION AND APPROXIMATION

Lagrangian Polynomials

Divided differences

Interpolating with a cubic spline

Newton’s forward difference formula

Newton’s backward difference formula

 

UNIT III

NUMERICAL DIFFERENTIATION AND

INTEGRATION

Differentiation using interpolation formulae

Numerical integration by trapezoidal rule

Simpson’s 1/3 and 3/8 rules

Romberg’s method

Two and Three point Gaussian quadrature formulas

Double integrals using trapezoidal and simpsons’s rules.

 UNIT IV
INITIAL VALUE PROBLEMS FOR
ORDINARY DIFFERENTIAL EQUATIONS
Taylor series method
Euler methods
Runge-Kutta method for solving first and second order equations
Milne’spredictor and corrector method
Adam’s predictor and corrector method.

UNIT V
BOUNDARY VALUE PROBLEMS IN
ORDINARY AND
PARTIALDIFFERENTIAL EQUATIONS
Finite difference solution of second order
ordinary differential equation
Finite difference solution of one dimensional
heat equation by explicit and implicit methods
One dimensional wave equation
Two dimensional Laplace equation
Poisson equation

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