Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.
Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact...
Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.
Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master ...
As it was already seen in the first volume of the present book, its guideline is precisely the mathematical model of mechanics. The classical models which we refer to are in fact models based on the Newtonian model of mechanics, on its five principles, i. e.: the inertia, the forces action, the action and reaction, the parallelogram and the initial conditions principle, respectively. Other models, e. g., the model of attraction forces between the particles of a discrete mechanical system, are part of the considered Newtonian model. Kepler s laws brilliantly verify this model in case of...
As it was already seen in the first volume of the present book, its guideline is precisely the mathematical model of mechanics. The classical models w...
The design and development of electrical devices involves choosing from many possible variants that which is the best or optimum according to one or several criteria. These optimization criteria are usually already clear to the designer at the statement of the design problem. The methods of optimization considered in this book, allow us to sort out variants of the realization of a design on the basis of these criteria and to create the best device in the sense of the set criteria. Optimization of devices is one of the major problems in electrical engi neering that is related to an extensive...
The design and development of electrical devices involves choosing from many possible variants that which is the best or optimum according to one or s...
Boundary Element Methods (BEM) play an important role in modern numerical computations in the applied and engineering sciences. These methods turn out to be powerful tools for numerical studies of various physical phenomena which can be described mathematically by partial differential equations.
The most prominent example is the potential equation (Laplace equation), which is used to model physical phenomena in electromagnetism, gravitation theory, and in perfect fluids. A further application leading to the Laplace equation is the model of steady state heat flow. One of the most...
Boundary Element Methods (BEM) play an important role in modern numerical computations in the applied and engineering sciences. These methods turn ...
All phenomena in nature are characterized by motion; this is an essential property of matter, having infinitely many aspects. Motion can be mechanical, physical, chemical or biological, leading to various sciences of nature, mechanics being one of them. Mechanics deals with the objective laws of mechanical motion of bodies, the simplest form of motion.
In the study of a science of nature mathematics plays an important role. Mechanics is the first science of nature which was expressed in terms of mathematics by considering various mathematical models, associated to phenomena of the...
All phenomena in nature are characterized by motion; this is an essential property of matter, having infinitely many aspects. Motion can be mechani...
Deformable solids have a particularly complex character; mathematical modeling is not always simple and often leads to inextricable difficulties of computation. One of the simplest mathematical models and, at the same time, the most used model, is that of the elastic body - especially the linear one. But, notwithstanding its simplicity, even this model of a real body may lead to great difficulties of computation.
The practical importance of a work about the theory of elasticity, which is also an introduction to the mechanics of deformable solids, consists of the use of scientific methods...
Deformable solids have a particularly complex character; mathematical modeling is not always simple and often leads to inextricable difficulties of...
This book deals with mathematically solving the unsteady flame propagation. New original mathematical methods for solving complex non-linear equations and investigating their properties are presented. Pole solutions for flame front propagation are developed. Premixed flames and filtration combustion have remarkable properties: The complex nonlinear integro-differential equations for this problem have exact analytical solutions to describe the motion of poles in a complex plane. Instead of complex equations, a finite set of ordinary differential equations is applied. These solutions help to...
This book deals with mathematically solving the unsteady flame propagation. New original mathematical methods for solving complex non-linear equations...
Covering classical elasticity theory in an encyclopaedic fashion, this work has been written by one of the world's leading authorities in the field and reflects the particularly complex character of deformable solids, where computer modeling is rarely simple.
Covering classical elasticity theory in an encyclopaedic fashion, this work has been written by one of the world's leading authorities in the field an...
This book deals with the problem of dynamics of bodies with time-variable mass and moment of inertia. Mass addition and mass separation from the body are treated. Dynamics of constant body is adopted, and the characteristics of the mass variation of the body is included. The chaotic motion of bodies with variable mass is discussed too.
This book deals with the problem of dynamics of bodies with time-variable mass and moment of inertia. Mass addition and mass separation from the body ...
