Decomposition Analysis Method in Linear and Nonlinear Differential Equations

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