Decomposition Analysis Method in Linear and Nonlinear Differential Equations  book cover
1st Edition

Decomposition Analysis Method in Linear and Nonlinear Differential Equations

ISBN 9781498716338
Published October 16, 2015 by Chapman & Hall
290 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. Asymptotic Decomposition. Bessel’s Equation. Navier-Stokes Equations in Cartesian Coordinates. Navier-Stokes Equations in Cylindrical Polar Coordinates. Blood Flow in Artery. Steady Subsonic Flow. Steady Transonic Flow. Laplace’s Equation. Flow Near a Rotating Disc in a Fluid at Rest. Appendix. Index.

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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.