Advanced Numerical Methods


Author: Moorthy M B K

ISBN: 9789388005067

Copy Right Year: 2019

Pages:  246

Binding: Soft Cover

Publisher:  Yes Dee Publishing

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This book offers a clear exposition of advanced mathematical methods. It is designed as a text book for this subject taught across PG courses offered at Anna University, Chennai and affiliated colleges. Basic concepts are explained briefly. Each topic is illustrated through a number of solved examples. Problems from the recent question papers of Anna University are presented either as solved examples or exercises with answers. Detailed hints and solutions of the problems are given for the benefit of the students.

Additional information

Weight .32 kg
Dimensions 23 × 18 × 1 cm

Table of Content

Chapter 1 Algebraic Equations
1.1 Introduction
1.2 Direct Methods in Solving System of Simultaneous Equations
1.2.1 Gauss Elimination Method
1.2.2 Thomas Algorithm for Tridiagonal Matrix
1.3 Indirect Method or Iterative Method in Solving a System of Linear
1.3.1 Gauss−Seidel and Gauss−Jacobi Method
1.3.2 Successive Over-Relaxation Method (SOR Method)
1.3.3 System of Non-linear Equations−Newton’s Method
1.3.4 Fixed Point Iterations
1.3.5 Eigen value Problem−Power Method
1.3.6 Faddeev−LeVerrier Method
Chapter 2 Ordinary Differential Equations
2.1 Initial Value Problems (IVPs)
2.1.1 Runge−Kutta Method (R−K Method) (Single-step Method)
2.1.2 Numerical Stability of Runge−Kutta Method
2.1.3 Adams−Bashforth Multi-step Method (Predictor−corrector Method)
2.2 Boundary Value Problems (BVP)
2.2.1 Finite Difference Method
2.2.2 Collocation Method
2.2.3 Galerkin Finite Element Method
2.2.4 Shooting Method
2.2.5 Orthogonal Collocation Method (OCM)
2.2.6 Orthogonal Collocation on Finite Elements (OCFE)
Chapter 3 Finite Difference Method for Time Dependent Partial Differential Equation
3.1 Finite Difference Solution for One-dimensional Heat Conduction Equation
(Parabolic Equation)
3.1.1 Finite Difference Explicit Scheme for One-dimensional Heat Conduction
3.1.2 Finite Difference Implicit Scheme (Crank−Nicolson Difference Method)
3.1.3 Dirichlet and Neumann Conditions
3.1.4 Two-dimensional Parabolic Equation
3.1.5 Alternating Direction Implicit (ADI) Method
3.1.6 Stability Analysis (Von Neumann)
3.2 Finite Difference Solution for Hyperbolic Equations
3.2.1 Numerical Solution for One-dimensional Wave Equation (Explicit
3.2.2 Derive the Finite Difference Explicit Scheme for One-dimensional Wave
3.2.3 First-order Hyperbolic Equations
Chapter 4 Finite Difference Methods for Elliptic Equations
4.1 Finite Difference Scheme for Two-dimensional Heat Conduction Equation in Steady State (Laplace Equation) and Poisson Equation
4.2 Dirichlet and Neumann Conditions
4.3 Problems on Mixed Boundary Value Problem
4.4 Laplace Equation in Polar Coordinates
Chapter 5 Finite Element Method −for PDEs
5.1 Finite Elements
5.1.1 Linear Element
5.1.2 Triangular Element
5.1.3 Rectangular Element
5.2 Galerkin Method
5.2.1 Galerkin Method (One Parameter Approximate Solution of BVP)
5.2.2 Collocation Method
5.2.3 Finite Element Methods (Orthogonal Collocation Method)
5.2.4 Finite Element Method−Orthogonal Collocation on Finite Elements

• Exercises

About The Author

Dr. M. B. K. Moorthy was Professor and Head at Department of Mathematics, Institute of Road and Transport Technology, Erode which is an automobile research oriented Institute. He has obtained his M.Sc., M.Phil., and Ph.D. in Applied Mathematics from Anna University, Chennai, and also holds an M.B.A. in HRM and M.Tech. in Computer Science and Engineering. He has over 36 years of experience in teaching at engineering colleges for both UG and PG students. He was a visiting professor at ISTE, New Delhi. He has published many research papers in national and international journals. He is a recognized guide for M.S/Ph.D. programs of Anna University. Six students have successfully completed their Ph.D. programs under his guidance.


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