Constructive Methods for Linear and Nonlinear Boundary Value Problems for Analytic Functions

Author: v Mityushev
Publisher: CRC Press
ISBN: 9781584880578
Format: PDF, Mobi
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Constructive methods developed in the framework of analytic functions effectively extend the use of mathematical constructions, both within different branches of mathematics and to other disciplines. This monograph presents some constructive methods-based primarily on original techniques-for boundary value problems, both linear and nonlinear. From among the many applications to which these methods can apply, the authors focus on interesting problems associated with composite materials with a finite number of inclusions. How far can one go in the solutions of problems in nonlinear mechanics and physics using the ideas of analytic functions? What is the difference between linear and nonlinear cases from the qualitative point of view? What kinds of additional techniques should one use in investigating nonlinear problems? Constructive Methods for Linear and Nonlinear Boundary Value Problems serves to answer these questions, and presents many results to Westerners for the first time. Among the most interesting of these is the complete solution of the Riemann-Hilbert problem for multiply connected domains. The results offered in Constructive Methods for Linear and Nonlinear Boundary Value Problems are prepared for direct application. A historical survey along with background material, and an in-depth presentation of practical methods make this a self-contained volume useful to experts in analytic function theory, to non-specialists, and even to non-mathematicians who can apply the methods to their research in mechanics and physics.

Applied Nonlinear Analysis

Author: V. Lakshmikantham
Publisher: Elsevier
ISBN: 1483272060
Format: PDF, Mobi
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Applied Nonlinear Analysis contains the proceedings of an International Conference on Applied Nonlinear Analysis, held at the University of Texas at Arlington, on April 20-22, 1978. The papers explore advances in applied nonlinear analysis, with emphasis on reaction-diffusion equations; optimization theory; constructive techniques in numerical analysis; and applications to physical and life sciences. In the area of reaction-diffusion equations, the discussions focus on nonlinear oscillations; rotating spiral waves; stability and asymptotic behavior; discrete-time models in population genetics; and predator-prey systems. In optimization theory, the following topics are considered: inverse and ill-posed problems with application to geophysics; conjugate gradients; and quasi-Newton methods with applications to large-scale optimization; sequential conjugate gradient-restoration algorithm for optimal control problems with non-differentiable constraints; differential geometric methods in nonlinear programming; and equilibria in policy formation games with random voting. In the area of constructive techniques in numerical analysis, numerical and approximate solutions of boundary value problems for ordinary and partial differential equations are examined, along with finite element analysis and constructive techniques for accretive and monotone operators. In addition, the book explores turbulent fluid flows; stability problems for Hopf bifurcation; product integral representation of Volterra equations with delay; weak solutions of variational problems, nonlinear integration on measures; and fixed point theory. This monograph will be helpful to students, practitioners, and researchers in the field of mathematics.

Further Progress in Analysis

Author: International Society for Analysis, Applications, and Computation. Congress
Publisher: World Scientific
ISBN: 9812837329
Format: PDF, ePub
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The ISAAC (International Society for Analysis, its Applications and Computation) Congress, which has been held every second year since 1997, covers the major progress in analysis, applications and computation in recent years. In this proceedings volume, plenary lectures highlight the recent research results, while 17 sessions organized by well-known specialists reflect the state of the art of important subfields. This volume concentrates on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, inverse problems, functional differential and difference equations and integrable systems.

Progress in Analysis

Author: Heinrich G W Begehr
Publisher: World Scientific
ISBN: 9814485233
Format: PDF, ePub
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The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting. Contents: Volume 1: Function Spaces and Fractional Calculus (V I Burenkov & S Samko)Asymptotic Decomposition (Methods of Small Parameters, Averaging Theory) (J A Dubinski)Integral Transforms and Applications (S Saitoh et al.)Analytic Functionals, Hyperfunctions and Generalized Functions (M Morimoto & H Komatsu)Geometric Function Theory (G Kohr & M Kohr)omplex Function Spaces (R Aulaskari & I Laine)Value Distribution Theory and Complex Dynamics (C C Yang)Clifford Analysis (K Gürlebeck et al.)Octonions (T Dray & C Monogue)Nonlinear Potential Theory (O Martio)Classical and Fine Potential Theory, Holomorphic and Finely Holomorphic Functions (P Tamrazov)Differential Geometry and Control Theory for PDEs (B Gulliver et al.)Differential Geometry and Quantum Physics (-)Dynamical Systems (B Fiedler)Attractors for Partial Differential Equations (G Raugel)Spectral Theory of Differential Operators (B Vainberg)Pseudodifferential Operators, Quantization and Signal Analysis (M W Wong)Microlocal Analysis (B-W Schulze & M Korey) Volume 2: Complex and Functional Analytic Methods in PDEs (A Cialdea et al.)Geometric Properties of Solutions of PDEs (R Magnanini)Qualitative Properties of Solutions of Hyperbolic and Schrödinger Equations (M Reissig & K Yagdjian)Homogenization Moving Boundaries and Porous Media (A Bourgeat & R P Gilbert)Constructive Methods in Applied Problems (P Krutitskii)Waves in Complex Media (R P Gilbert & A Wirgin)Nonlinear Waves (I Lasiecka & H Koch)Mathematical Analysis of Problems in Solid Mechanics (K Hackl & X Li)Direct and Inverse Scattering (L Fishman)Inverse Problems (G N Makrakis et al.)Mathematical Methods in Non-Destructive Evaluation and Non-Destructive Testing (A Wirgin)Numerical Methods for PDEs, Systems and Optimization (A Ben-Israel & I Herrera) Readership: Graduate students and researchers in real, complex, numerical analysis, as well as mathematical physics.Keywords:Fractional Calculus;Function Theory;Potential Theory;Dynamical Systems;Differential Operators;Pseudodifferntial Operators;Partial Differential Equations;Inverse Problems

Progress in Analysis

Author: Heinrich G. W. Begehr
Publisher: World Scientific
ISBN: 981238572X
Format: PDF, Mobi
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The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.

Nonlinear Problems of Engineering

Author: William F. Ames
Publisher: Academic Press
ISBN: 148322581X
Format: PDF, ePub, Docs
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Nonlinear Problems of Engineering reviews certain nonlinear problems of engineering. This book provides a discussion of nonlinear problems that occur in four areas, namely, mathematical methods, fluid mechanics, mechanics of solids, and transport phenomena. Organized into 15 chapters, this book begins with an overview of some of the fundamental ideas of two mathematical theories, namely, invariant imbedding and dynamic programming. This text then explores nonlinear integral equations, which have long occupied a prominent place in mathematical analysis. Other chapters consider the phenomena associated with essentially divergent small-divisor series, such as may occur in the formal solution of differential equations that represent the oscillations of conservative dynamical systems. This book discusses as well the mechanics of idealized textiles consisting of inextensible filaments. The final chapter deals with the use of the Peaceman–Rachford alternating direction implicit method for solving the finite difference analogs of boundary value problems. This book is a valuable resource for engineers and mathematicians.

Numerical Solution of Differential Equations

Author: Isaac Fried
Publisher: Academic Press
ISBN: 1483262529
Format: PDF
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Numerical Solution of Differential Equations is a 10-chapter text that provides the numerical solution and practical aspects of differential equations. After a brief overview of the fundamentals of differential equations, this book goes on presenting the principal useful discretization techniques and their theoretical aspects, along with geometrical and physical examples, mainly from continuum mechanics. Considerable chapters are devoted to the development of the techniques of the numerical solution of differential equations and their analysis. The remaining chapters explore the influential invention in computational mechanics-finite elements. Each chapter emphasizes the relationship among the analytic formulation of the physical event, the discretization techniques applied to it, the algebraic properties of the discrete systems created, and the properties of the digital computer. This book will be of great value to undergraduate and graduate mathematics and physics students.

Numerical Analytic Methods in the Theory of Boundary Value Problems

Author: M Ronto
Publisher: World Scientific
ISBN: 9814495484
Format: PDF, Mobi
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This book contains the main results of the authors' investigations on the development and application of numerical-analytic methods for ordinary nonlinear boundary value problems (BVPs). The methods under consideration provide an opportunity to solve the two important problems of the BVP theory — namely, to establish existence theorems and to build approximation solutions. They can be used to investigate a wide variety of BVPs. The Appendix, written in collaboration with S I Trofimchuk, discusses the connection of the new method with the classical Cesari, Cesari–Hale and Lyapunov–Schmidt methods. Contents:Numerical-Analytic Method of Successive Approximations for Two-Point Boundary-Value ProblemsModification of the Numerical-Analytic Method for Two-Point Boundary-Value ProblemsNumerical-Analytic Method for Boundary-Value Problems with Parameters in Boundary ConditionsCollocation Method for Boundary-Value Problems with ImpulsesThe Theory of the Numerical-Analytic Method: Achievements and New Trends of Development Readership: Researchers on differential equations. Keywords:Ordinary Differential Equations;Nonlinear Boundary Value Problems;Periodic Boundary Value Problems;Nonlinear Boundary Conditions;Parametrized Boundary Value Problems;Numerical-Analytic Method;Successive Approximations;Determining Equations;Trigonometric Collocation;Impulsive Systems