Provides knowledge about Applied Numerical Methods in vit (Vellore Institute of Technology) VIT BHOPAL UNIVERSITY
#Overview
(1)
Algebraic, Transcendental and linear system of equations
Introduction to Direct and Iterative methods – (Fixed point) Iteration
method - order and condition of convergence - Secant and Newton- Raphson methods for simple roots – Rates of convergence - Gauss- Elimination – Thomas Algorithm for tridiagonal linear system of
equations - Gauss-Seidel iteration method - Diagonal dominance and convergence of Gauss-Seidel iteration method
(2)
Interpolation
Finite difference operators: Forward, Backward, Central, Average, Shift and Differential – Relation between these difference operators – Interpolation - Newton’s forward and backward Interpolations -– Lagrange Interpolation - Newton’s Divided Difference Interpolation - Cubic spline interpolation for a tabulated function with equally spaced data
(3)
Numerical Differentiation and Integration
Derivatives using Newton’s Forward and Backward interpolations – Newton-Cotes Quadrature rule - Trapezoidal rule, Simpson’s 1/3 and 3/8 rules – Gaussian Quadrature rule - Two point and three point Gauss-Legendre quadrature rules – composite quadrature rules - Romberg method
(4)
Numerical Solution of Ordinary Differential Equations
First order initial value problems - Taylor’s Series method - Euler’s method - Modified Euler’s method - Runge–Kutta method of fourth order - Adams-Bashforth predictor-corrector method - Finite difference method for second order boundary value problems
(5)
Numerical Solution of Partial Differential Equations
Classification of second order linear partial differential equations – Finite difference method – Explicit and Implicit methods - Schmidt and Crank-Nicolson methods for 1-D heat equation – Explicit method for 1-D wave equation – Liebmann’s iteration method for 2-D Laplace and Poisson equations
- Open Source Licenced
- For Educational Purpose