Decomposition Analysis Method in Linear and Nonlinear Differential Equations

NOTE EDITORE

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.

SOMMARIO

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 EquationIntroduction 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 CoordinatesIntroduction 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 PlatesPulsatile 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 FlowIntroduction 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 FlowFlow 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 ? Solutions for the Large Value of ? Appendix Index References appear at the end of each chapter.

AUTORE

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.

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9781498716338
• Dimensioni: 9.25 x 6.25 in Ø 1.37 lb
• Formato: Copertina rigida
• Illustration Notes: 20 b/w images
• Pagine Arabe: 274
• Pagine Romane: xvi