1st Edition

Decomposition Analysis Method in Linear and Nonlinear Differential Equations

By Kansari Haldar Copyright 2016
    290 Pages 20 B/W Illustrations
    by Chapman & Hall

    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.

    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.

    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.