Nonlinear Stochastic Operator Equations

Nonlinear Stochastic Operator Equations
Author: George Adomian
Publisher: Academic Press
Total Pages: 304
Release: 2014-05-09
Genre: Science
ISBN: 1483259099

Nonlinear Stochastic Operator Equations deals with realistic solutions of the nonlinear stochastic equations arising from the modeling of frontier problems in many fields of science. This book also discusses a wide class of equations to provide modeling of problems concerning physics, engineering, operations research, systems analysis, biology, medicine. This text discusses operator equations and the decomposition method. This book also explains the limitations, restrictions and assumptions made in differential equations involving stochastic process coefficients (the stochastic operator case), which yield results very different from the needs of the actual physical problem. Real-world application of mathematics to actual physical problems, requires making a reasonable model that is both realistic and solvable. The decomposition approach or model is an approximation method to solve a wide range of problems. This book explains an inherent feature of real systems—known as nonlinear behavior—that occurs frequently in nuclear reactors, in physiological systems, or in cellular growth. This text also discusses stochastic operator equations with linear boundary conditions. This book is intended for students with a mathematics background, particularly senior undergraduate and graduate students of advanced mathematics, of the physical or engineering sciences.

Applied Stochastic Differential Equations

Applied Stochastic Differential Equations
Author: Simo Särkkä
Publisher: Cambridge University Press
Total Pages: 327
Release: 2019-05-02
Genre: Business & Economics
ISBN: 1316510085

With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Backward Stochastic Differential Equations

Backward Stochastic Differential Equations
Author: N El Karoui
Publisher: CRC Press
Total Pages: 236
Release: 1997-01-17
Genre: Mathematics
ISBN: 9780582307339

This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.

Nonlinear Fokker-Planck Equations

Nonlinear Fokker-Planck Equations
Author: T.D. Frank
Publisher: Springer Science & Business Media
Total Pages: 414
Release: 2005-01-07
Genre: Science
ISBN: 3540212647

Centered around the natural phenomena of relaxations and fluctuations, this monograph provides readers with a solid foundation in the linear and nonlinear Fokker-Planck equations that describe the evolution of distribution functions. It emphasizes principles and notions of the theory (e.g. self-organization, stochastic feedback, free energy, and Markov processes), while also illustrating the wide applicability (e.g. collective behavior, multistability, front dynamics, and quantum particle distribution). The focus is on relaxation processes in homogeneous many-body systems describable by nonlinear Fokker-Planck equations. Also treated are Langevin equations and correlation functions. Since these phenomena are exhibited by a diverse spectrum of systems, examples and applications span the fields of physics, biology and neurophysics, mathematics, psychology, and biomechanics.

Nonlinear Stochastic Systems Theory and Applications to Physics

Nonlinear Stochastic Systems Theory and Applications to Physics
Author: G. Adomian
Publisher: Springer Science & Business Media
Total Pages: 248
Release: 1988-12-31
Genre: Mathematics
ISBN: 902772525X

Approach your problems from the right end and begin with the answers. Then one day, perhaps you will find the final answer. "The Hermit Clad In Crane Feathers" In R. van Gullk's The Chinese Haze Hurders. It Isn't that they can't see the solution. It IS that they can't see the problem. G. K. Chesterton. The Scandal of Father Brown. "The POint of a Pin." Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of k now ledge of m athemat i cs and re I ated fie I ds does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, COding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And In addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely Integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the eXisting classificatIOn schemes.

Nonlinear Stochastic Systems In Physics And Mechanics

Nonlinear Stochastic Systems In Physics And Mechanics
Author: Nicola Bellomo
Publisher: World Scientific
Total Pages: 260
Release: 1987-03-01
Genre: Science
ISBN: 9813104295

This book presents the conceptional line which goes from the observation of physical systems to their modeling and analysis by ordinary differential nonlinear stochastic equations.First, the problems of the mathematical modeling of physical systems are developed. These mathematical models are then classified in terms of ordinary differential stochastic equations from which both qualitative and quantitative results are developed.Each one of the various subjects are methods dealt with ends with an application in mathematical physics or in nonlinear mechanics.

An Introduction to Nonlinear Analysis and Fixed Point Theory

An Introduction to Nonlinear Analysis and Fixed Point Theory
Author: Hemant Kumar Pathak
Publisher: Springer
Total Pages: 845
Release: 2018-05-19
Genre: Mathematics
ISBN: 9811088667

This book systematically introduces the theory of nonlinear analysis, providing an overview of topics such as geometry of Banach spaces, differential calculus in Banach spaces, monotone operators, and fixed point theorems. It also discusses degree theory, nonlinear matrix equations, control theory, differential and integral equations, and inclusions. The book presents surjectivity theorems, variational inequalities, stochastic game theory and mathematical biology, along with a large number of applications of these theories in various other disciplines. Nonlinear analysis is characterised by its applications in numerous interdisciplinary fields, ranging from engineering to space science, hydromechanics to astrophysics, chemistry to biology, theoretical mechanics to biomechanics and economics to stochastic game theory. Organised into ten chapters, the book shows the elegance of the subject and its deep-rooted concepts and techniques, which provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in diverse applied fields. It is intended for graduate and undergraduate students of mathematics and engineering who are familiar with discrete mathematical structures, differential and integral equations, operator theory, measure theory, Banach and Hilbert spaces, locally convex topological vector spaces, and linear functional analysis.

Partial Differential Equations

Partial Differential Equations
Author: N.D. Bellman
Publisher: Springer Science & Business Media
Total Pages: 306
Release: 2012-12-06
Genre: Mathematics
ISBN: 9400952090

The purpose of this book is to present some new methods in the treatment of partial differential equations. Some of these methods lead to effective numerical algorithms when combined with the digital computer. Also presented is a useful chapter on Green's functions which generalizes, after an introduction, to new methods of obtaining Green's functions for partial differential operators. Finally some very new material is presented on solving partial differential equations by Adomian's decomposition methodology. This method can yield realistic computable solutions for linear or non linear cases even for strong nonlinearities, and also for deterministic or stochastic cases - again even if strong stochasticity is involved. Some interesting examples are discussed here and are to be followed by a book dealing with frontier applications in physics and engineering. In Chapter I, it is shown that a use of positive operators can lead to monotone convergence for various classes of nonlinear partial differential equations. In Chapter II, the utility of conservation technique is shown. These techniques are suggested by physical principles. In Chapter III, it is shown that dyn~mic programming applied to variational problems leads to interesting classes of nonlinear partial differential equations. In Chapter IV, this is investigated in greater detail. In Chapter V, we show. that the use of a transformation suggested by dynamic programming leads to a new method of successive approximations.

Nonlinear Equations in Abstract Spaces

Nonlinear Equations in Abstract Spaces
Author: V. Lakshmikantham
Publisher: Elsevier
Total Pages: 494
Release: 2014-05-27
Genre: Mathematics
ISBN: 1483272109

Many problems in partial differential equations which arise from physical models can be considered as ordinary differential equations in appropriate infinite dimensional spaces, for which elegant theories and powerful techniques have recently been developed. This book gives a detailed account of the current state of the theory of nonlinear differential equations in a Banach space, and discusses existence theory for differential equations with continuous and discontinuous right-hand sides. Of special importance is the first systematic presentation of the very important and complex theory of multivalued discontinuous differential equations.

Dynamic Modelling and Control of National Economies 1983

Dynamic Modelling and Control of National Economies 1983
Author: T. Basar
Publisher: Elsevier
Total Pages: 489
Release: 2014-05-17
Genre: Business & Economics
ISBN: 1483153312

Dynamic Modelling and Control of National Economies 1983 contains the proceedings of the Fourth IFAC/IFORS/IIASA Conference and the 1983 SEDC Conference on Economic Dynamics and Control held at Washington D.C., USA on June17-19, 1983. Separating the 65 papers presented in the conference as chapters, this book covers a broad class of problems or notions arising both in economic theory, control applications to planning, and implementation issues. Some chapters discuss multi-level interactions of government and private sectors in economic development; inflation and economic policy in an open economy; foreign debt and exchange rate stability in a developing country; and expectations in numerical general equilibrium models. This book also explains a rational decision-making process for resource policymaking; inference of the structure of economic reasoning from natural language analysis; modeling and analysis of a national economy; and methodological issues in global modeling. Econometric analysis of the economic effects of population change, aspects of optimal estimation control strategies in econometrics, and optimal policies for interdependent economies are also discussed. This book will be useful to those engaged in economic and control theory research.