Applications of Differential Transform to Real World Problems
Applications of Differential Transform to Real World Problems

Author: Yogeshwari F Patel

Publisher: CRC Press

Published: 2022-08-08

Total Pages: 307

ISBN-13: 1000629562

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This book is an invaluable resource for applied researchers to find the analytical solution of differential equations describing the dynamical system with less computational effort and time. It describes the basic concepts of the differential transform method and solution of various real-world problems described by simple to complicated differential equations. It provides a computational technique that is not only conceptually simple and easy to use but also readily adaptable for computer coding. Different chapters of the book deal with the basic differential equations involved in the physical phenomena as well as a complicated system of differential equations described by the mathematical model. The book offers comprehensive coverage of the most essential topics, including Basic concepts and fundamental properties of the proposed technique with proof The solution of linear, nonlinear, homogeneous, and nonhomogeneous ordinary differential equations (ODEs) and partial differential equations (PDEs) The initial and boundary value problems Real-world ODE and PDE problems are also discussed Applications of Differential Transform to Real World Problems is primarily aimed at undergraduates, graduates, and researchers studying differential equations. Scientists dealing with complicated differential equations or systems of differential equations will also find this book useful.

500 Examples and Problems of Applied Differential Equations
500 Examples and Problems of Applied Differential Equations

Author: Ravi P. Agarwal

Publisher: Springer Nature

Published: 2019-09-24

Total Pages: 394

ISBN-13: 3030263843

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This book highlights an unprecedented number of real-life applications of differential equations together with the underlying theory and techniques. The problems and examples presented here touch on key topics in the discipline, including first order (linear and nonlinear) differential equations, second (and higher) order differential equations, first order differential systems, the Runge–Kutta method, and nonlinear boundary value problems. Applications include growth of bacterial colonies, commodity prices, suspension bridges, spreading rumors, modeling the shape of a tsunami, planetary motion, quantum mechanics, circulation of blood in blood vessels, price-demand-supply relations, predator-prey relations, and many more. Upper undergraduate and graduate students in Mathematics, Physics and Engineering will find this volume particularly useful, both for independent study and as supplementary reading. While many problems can be solved at the undergraduate level, a number of challenging real-life applications have also been included as a way to motivate further research in this vast and fascinating field.

Differential Transformation Method for Mechanical Engineering Problems
Differential Transformation Method for Mechanical Engineering Problems

Author: Mohammad Hatami

Publisher: Academic Press

Published: 2016-11-17

Total Pages: 424

ISBN-13: 0128053402

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Differential Transformation Method for Mechanical Engineering Problems focuses on applying DTM to a range of mechanical engineering applications. The authors modify traditional DTM to produce two additional methods, multi-step differential transformation method (Ms-DTM) and the hybrid differential transformation method and finite difference method (Hybrid DTM-FDM). It is then demonstrated how these can be a suitable series solution for engineering and physical problems, such as the motion of a spherical particle, nanofluid flow and heat transfer, and micropolar fluid flow and heat transfer. - Presents the differential transformation method and why it holds an advantage over higher-order Taylor series methods - Includes a full mathematical introduction to DTM, Ms-DTM, and Hybrid DTM - Covers the use of these methods for solving a range of problems in areas such as nanofluid flow, heat transfer, and motion of a spherical particle in different conditions - Provides numerous examples and exercises which will help the reader fully grasp the practical applications of these new methods

Applications of Nanofluid for Heat Transfer Enhancement
Applications of Nanofluid for Heat Transfer Enhancement

Author: Mohsen Sheikholeslami

Publisher: William Andrew

Published: 2017-02-26

Total Pages: 620

ISBN-13: 0128123982

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Applications of Nanofluid for Heat Transfer Enhancement explores recent progress in computational fluid dynamic and nonlinear science and its applications to nanofluid flow and heat transfer. The opening chapters explain governing equations and then move on to discussions of free and forced convection heat transfers of nanofluids. Next, the effect of nanofluid in the presence of an electric field, magnetic field, and thermal radiation are investigated, with final sections devoted to nanofluid flow in porous media and application of nanofluid for solidification. The models discussed in the book have applications in various fields, including mathematics, physics, information science, biology, medicine, engineering, nanotechnology, and materials science. - Presents the latest information on nanofluid free and force convection heat transfer, of nanofluid in the presence of thermal radiation, and nanofluid in the presence of an electric field - Provides an understanding of the fundamentals in new numerical and analytical methods - Includes codes for each modeling method discussed, along with advice on how to best apply them

Fractional Dynamics
Fractional Dynamics

Author: Carlo Cattani

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2015-01-01

Total Pages: 392

ISBN-13: 3110472090

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The book is devoted to recent developments in the theory of fractional calculus and its applications. Particular attention is paid to the applicability of this currently popular research field in various branches of pure and applied mathematics. In particular, the book focuses on the more recent results in mathematical physics, engineering applications, theoretical and applied physics as quantum mechanics, signal analysis, and in those relevant research fields where nonlinear dynamics occurs and several tools of nonlinear analysis are required. Dynamical processes and dynamical systems of fractional order attract researchers from many areas of sciences and technologies, ranging from mathematics and physics to computer science.

Beyond Perturbation
Beyond Perturbation

Author: Shijun Liao

Publisher: CRC Press

Published: 2003-10-27

Total Pages: 335

ISBN-13: 1135438293

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Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, and even perturbation approximations are valid only for problems with weak nonlinearity. This book introduces a powerful new analytic method for nonlinear problems-homotopy analysis-that remains valid even with strong nonlinearity. In Part I, the author starts with a very simple example, then presents the basic ideas, detailed procedures, and the advantages (and limitations) of homotopy analysis. Part II illustrates the application of homotopy analysis to many interesting nonlinear problems. These range from simple bifurcations of a nonlinear boundary-value problem to the Thomas-Fermi atom model, Volterra's population model, Von Karman swirling viscous flow, and nonlinear progressive waves in deep water. Although the homotopy analysis method has been verified in a number of prestigious journals, it has yet to be fully detailed in book form. Written by a pioneer in its development, Beyond Pertubation: Introduction to the Homotopy Analysis Method is your first opportunity to explore the details of this valuable new approach, add it to your analytic toolbox, and perhaps make contributions to some of the questions that remain open.

Elementary Differential Equations
Elementary Differential Equations

Author: William E. Boyce

Publisher: John Wiley & Sons

Published: 2017-08-14

Total Pages: 512

ISBN-13: 1119443636

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With Wiley's Enhanced E-Text, you get all the benefits of a downloadable, reflowable eBook with added resources to make your study time more effective, including: Embedded & searchable equations, figures & tables Math XML Index with linked pages numbers for easy reference Redrawn full color figures to allow for easier identification Elementary Differential Equations, 11th Edition is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two ] or three ] semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.

Textbook on Ordinary Differential Equations
Textbook on Ordinary Differential Equations

Author: Ramakanta Meher

Publisher: CRC Press

Published: 2022-12-29

Total Pages: 290

ISBN-13: 1000824020

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Many scientific and real-world problems that occur in science, engineering, and medicine can be represented in differential equations. There is a vital role for differential equations in studying the behavior of different types of real-world problems. Thus, it becomes crucial to know the existence and uniqueness properties of differential equations and various methods of finding differential equation solutions in explicit form. It is also essential to know different kinds of differential equations in terms of eigenvalues, termed eigenvalue problems, and some special functions used in finding the solution to differential equations. The study of nonlinear problems also plays a significant role in different real-world situations. There is a necessity to know the behavior of solutions of nonlinear differential equations. Still, there are very few forms of differential equations whose solution can be found in explicit form. For the differential equations whose solutions cannot be found in explicit form, one has to study the properties of solutions of the given differential equation to guess an approximate solution of it. This book aims to introduce all the necessary topics of differential equations in one book so that laymen can easily understand the subject and apply it in their research areas. The novel approach used in this book is the introduction of different analytical methods for finding the solution of differential equations with sufficient theorems, corollaries, and examples, and the geometrical interpretations in each topic. This textbook is intended to study the theory and methods of finding the explicit solutions to differential equations, wherever possible, and in the absence of finding explicit solutions, it is intended to study the properties of solutions to the given differential equations. This book is based on syllabi of the theory of differential equations prescribed for postgraduate students of mathematics and applied mathematics in different institutions and universities of India and abroad. This book will be helpful for competitive examinations as well.

Fixed Point Theory and Fractional Calculus
Fixed Point Theory and Fractional Calculus

Author: Pradip Debnath

Publisher: Springer Nature

Published: 2022-05-10

Total Pages: 358

ISBN-13: 9811906688

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This book collects chapters on fixed-point theory and fractional calculus and their applications in science and engineering. It discusses state-of-the-art developments in these two areas through original new contributions from scientists across the world. It contains several useful tools and techniques to develop their skills and expertise in fixed-point theory and fractional calculus. New research directions are also indicated in chapters. This book is meant for graduate students and researchers willing to expand their knowledge in these areas. The minimum prerequisite for readers is the graduate-level knowledge of analysis, topology and functional analysis.