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This book bring new solutions for various types of differential equations. Approximate analytic solution was obtained for system of differential equations specially that has chaotic behavior, delay differential equations, Schrodinger and coupled Schrodinger equation, fractional differential equations, differential algebraic equations and some other fluid mechanic models. Accurate and simple solution was presented via several modifications for homotopy analysis method.
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order.
Evolutionary Dynamics – Exploring the Equations of Life
The importance of partial differential equations cannot be gainsaid. They are used in science and engineering. Many natural phenomena such as sound, heat, electrostatics, electrodynamics, fluid flow etc occurring in science and engineering are described by partial differential equations. Partial differential equations often model mathematical systems where many variables exist. They are also used in statistics especially in the field of stochastic processes.
Designed for advanced undergraduate and graduate students in applied mathematics as well as researchers, this illuminating resource will introduce the reader to the fundamental aspects of three powerful iterative methods for handling equations with distinct structures. The book will serve nicely as a supplementary textbook for course study. The aim of this textbook is threefold: firstly, give a detailed review of the Adomian Decomposition Method for solving linear/nonlinear ordinary and partial differential equations, algebraic equations, delay differential equations, linear and nonlinear integral equations, and integro-differential equations. Secondly, the essential features of the He’s Variational Iteration Method are rigorously presented for solving a wide spectrum of equations. Finally, introduce a novel method based on manipulating Green’s functions and some popular fixed point iterations schemes, such as Picard's and Mann's, for the numerical solution of boundary value problems.
An Introduction to Difference Equations, Differential Equations and Modeling give us an overview of studies in difference equations, differential equations with piecewise constant arguments and about some biological models. Here, they will see important relations between difference equations and differential equations with piecewise constant arguments, and biological events that are explained with mathematics. It is my hope that this work can be useful for students or researcher that are interested in Biomathematics.
Nonlinear difference equations of order greater than one are of paramount importance in applications. Such equations appear naturally as a discrete analogues and as numerical solutions of differential equations and delay differential equations. They have models in various diverse phenomena in biology, ecology, physiology, physics, engineering and economics. Our goal in this thesis is understanding the dynamics of nonlinear difference equations to construct the basic theory of this ?led. We believe that the results of this thesis are prototypes towards the development of the basic theory of the global behavior of solutions of nonlinear difference equations of order greater than one. Now we are going to give some examples for applications of difference equations.
In this book the existence and uniqueness of fuzzy linear integro-differential equations of Volterra type is proved, also the analytic, approximated, and numerical solutions of these type of equations are discussed. Also the concept of fuzzy reduction formula to reduce fuzzy linear differential equations, fuzzy linear Volterra integral equations, and high order fuzzy linear integro-differential equations of Volterra type to first order fuzzy linear integro-differential equations of Volterra type are introduced. Tow type of fuzzy functions are used to define functions in each equation, fuzzy valued functions and fuzzy bunch function.
In this book is presented a new method introduced in order to establish solutions for fractional differential equations. This method is based on a combination of Adomian decomposition method and Laplace transform method. This new method can be applied to linear and nonlinear fractional differential equations. The method is illustrated on a series of examples including ordinary differential equations and systems of differential equations, partial differential equations and systems. The method can be used with the aid of symbolic calculus. For this reason we are suggested some Maple and Mathematica solutions of the examples investigated.
The theory of integral equations has a close contact with many different areas of mathematics. This is sufficient to say that there is almost no area of applied sciences and physics where integral equations do not play an important role. This books intended primarily to study the existence of solution , analytically and numerically, of nonlinear integral equations of the second kind of types Hammerstein, Hammerstein- Volterra and Volterra-Hammerstein. Also, it is used for proving the existence and uniqueness solution, analytically, of linear integro-differential and integral equations of type Fredholm-Volterra in three dimensional. Finally, it is very useful in establishing the existence and uniqueness solution of linear and nonlinear partial differential equations of fractional order, analytically and numerically.
This book is devoted to study multidimensional linear and nonlinear partial differential equations. Among several methods to deal with higher dimensional linear partial differential equations, the elegant method of Spherical Means has spacial importance since this method reduces the higher dimensional equations to the one dimensional radial equations of Euler-Poisson-Darboux type which are well studied. Although this method is applicable only to the linear differential equations, by some special transformations, like the Cole-Hopf transformation and the Backlaund transformation, exact solutions of multidimensional nonlinear partial differential equations of the Spherical Liouville, Sine- Gordon and Burgers type are constructed.
The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
Most problems in engineering and science are modeled by partial differential equations. These partial differential equations often contain non-linearities and stochastic terms which makes their analytical solution cumbersome and sometimes nonexistent. We present a basic intoduction to using semi-analtyic-numerical methods to solve this partial differential equations and hence understanding the nature of the problems they describe.
This book covers the basic discussions on ordinary differential equations as fundamentals for the study of differential equations. This consists of the lessons together with sample problems and exercises at the end of every topic to give way the student for him to solve it. It is important that the student gain not just how to solve problems but most importantly, student should gain the concepts and ideas behind a certain topic. The author wishes that with this material, students can learn fully the knowledge of ordinary differential equations.
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps and provides all the necessary details. Topical coverage includes: First-Order Differential Equations Higher-Order Linear Equations Applications of Higher-Order Linear Equations Systems of Linear Differential Equations Laplace Transform Series Solutions Systems of Nonlinear Differential Equations In addition to plentiful exercises and examples throughout, each chapter concludes with a summary that outlines key concepts and techniques. The book's design allows readers to interact with the content, while hints, cautions, and emphasis are uniquely featured in the margins to further help and engage readers. Written in an accessible style that includes all needed details and steps, Ordinary Differential Equations is an excellent book for courses on the topic at the upper-undergraduate level. The book also serves as a valuable resource for professionals in the fields of engineering, physics, and mathematics who utilize differential equations in their everyday work. An Instructors Manual is available upon request. Email email@example.com for information. There is also a Solutions Manual available. The ISBN is 9781118398999.