Decomposition Analysis Method in Linear and Nonlinear Differential Equations  book cover
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Decomposition Analysis Method in Linear and Nonlinear Differential Equations




ISBN 9781498716338
Published October 16, 2015 by Chapman and Hall/CRC
274 Pages 20 B/W Illustrations

 
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Book Description

A Powerful Methodology for Solving All Types of Differential Equations

Decomposition Analysis Method in Linear and Non-Linear Differential Equations explains how the Adomian decomposition method can solve differential equations for the series solutions of fundamental problems in physics, astrophysics, chemistry, biology, medicine, and other scientific areas. This method is advantageous as it simplifies a real problem to reduce it to a mathematically tractable form.

The book covers the four classes of the decomposition method: regular/ordinary decomposition, double decomposition, modified decomposition, and asymptotic decomposition. It applies these classes to Laplace and Navier–Stokes equations in Cartesian and polar coordinates for obtaining partial solutions of the equations. Examples of physical and physiological problems, such as tidal waves in a channel, fluids between plates and through tubes, the flow of blood through arteries, and the flow past a wave-shaped wall, demonstrate the applications.

Drawing on the author’s extensive research in fluid and gas dynamics, this book shows how the powerful decomposition methodology of Adomian can solve differential equations in a way comparable to any contemporary superfast computer.

Table of Contents

Decomposition Method
Introduction
Partial Solutions of a Partial Differential Equation
A Review on the Convergence of the Decomposition Method

Asymptotic Decomposition
Introduction
Application of Asymptotic Decomposition

Bessel’s Equation
Introduction
Solution of Bessel’s General Equation by Modified Decomposition
Second Solution of Bessel’s Equation by Regular Decomposition
Pulsatile Flow of Fluid in a Rigid Tube
Periodic Motion of a Visco-Elastic Fluid in a Rigid Tube
Tidal Waves in a Channel Open to the Sea
Temperature Distribution in an Infinitely Long Circular Cylinder

Navier-Stokes Equations in Cartesian Coordinates
Introduction
Equations of Motion
Steady Laminar Flow of Viscous Fluid through a Tube of an Elliptic Cross Section
Stokes’s First Problem: The Suddenly Accelerated Plane Wall
Stokes’s Second Problem: The Flow Near an Oscillating Flat Plate
Unsteady Flow of Viscous Incompressible Fluid between Two Parallel Plates
Pulsatile Flow between Two Parallel Plates

Navier-Stokes Equations in Cylindrical Polar Coordinates
Introduction
Equations of Motion
Hagen-Poiseuille Theory: The Steady Laminar Flow of Fluid through a Circular Tube
Couette Flow: Steady Laminar Flow between Two Concentric Rotating Circular Cylinders
Flow in Convergent and Divergent Channels

Blood Flow in Artery
Introduction
Steady Flow of Blood through a Constricted Artery
Flow of Blood through Arteries in the Presence of a Magnetic Field
Pulsatile Flow of Blood through a Constricted Artery

Steady Subsonic Flow
Introduction
Equations of Motion
Application of Regular Decomposition to a Linearized Gasdynamic Equation for Plane Flow
Application of Modified Decomposition to a Linearized Gasdynamic Equation for Plane Flow
Flow Past a Wavy Wall
Application of Regular Decomposition to a Linearized Gasdynamic Equation for Axisymmetric Flow
Flow Past a Corrugated Circular Cylinder

Steady Transonic Flow
Introduction
Transonic Solution by Regular Decomposition
Transonic Solution by Modified Decomposition
Transonic Solution by Multidimensional Operator
Transonic Flow Past a Wavy Wall

Laplace’s Equation
Introduction
Solution of Laplace’s Equation by Regular Decomposition
Solution of Laplace’s Equation by Modified Decomposition
Laplace’s Equation for a Circular Disc
Laplace’s Equation for a Circular Annulus

Flow Near a Rotating Disc in a Fluid at Rest
Introduction
Equations of Motion
Solutions for the Small Value of η
Solutions for the Large Value of η

Appendix

Index

References appear at the end of each chapter.

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Author(s)

Biography

Kansari Haldar retired as a professor from the Indian Statistical Institute, Kolkata. His work has spanned 35 years, covering fluid dynamics, gas dynamics, hydrodynamics, biofluid dynamics, biomagnetofluid dynamics, and Adomian’s decomposition methodology.