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New Difference Schemes for Partial Differential Equations

Posted By: AvaxGenius
New Difference Schemes for Partial Differential Equations

New Difference Schemes for Partial Differential Equations by Allaberen Ashyralyev , Pavel E. Sobolevskii
English | PDF | 2004 | 453 Pages | ISBN : 3764370548 | 48.7 MB

The present monograph is devoted to the construction and investigation of the new high order of accuracy difference schemes of approximating the solutions of regular and singular perturbation boundary value problems for partial differential equations. The construction is based on the exact difference scheme and Taylor's decomposition on the two or three points. This approach permitted essentially to extend to a class of problems where the theory of difference methods is applicable. Namely, now it is possible to investigate the differential equations with variable coefficients and regular and singular perturbation boundary value problems. The investigation is based on new coercivity inequalities.

My Mathematical Life: Yuan Wang in Conversation

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My Mathematical Life: Yuan Wang in Conversation

My Mathematical Life: Yuan Wang in Conversation by Yuan Wang
English | PDF EPUB (True) | 2024 | 114 Pages | ISBN : 9811935505 | 4.7 MB

This book is an autobiographical interview with Chinese Academician Yuan Wang on his experience in mathematical research. The book looks back on Wang's collaboration with his teacher Hua Loo-Keng and younger scholars, offering insights into fruitful cooperation in mathematical research.

Modeling with Itô Stochastic Differential Equations (Repost)

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Modeling with Itô Stochastic Differential Equations (Repost)

Modeling with Itô Stochastic Differential Equations by E. Allen
English | PDF | 2007 | 238 Pages | ISBN : 1402059523 | 1.6 MB

Dynamical systems with random influences occur throughout the physical, biological, and social sciences. By carefully studying a randomly varying system over a small time interval, a discrete stochastic process model can be constructed. Next, letting the time interval shrink to zero, an Ito stochastic differential equation model for the dynamical system is obtained.

Metaheuristic Procedures for Training Neural Networks (Repost)

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Metaheuristic Procedures for Training Neural Networks (Repost)

Metaheuristic Procedures for Training Neural Networks by Enrique Alba, Rafael Martí
English | PDF | 2007 | 258 Pages | ISBN : 0387334157 | 11.7 MB

Metaheuristic Procedures For Training Neural Networks provides successful implementations of metaheuristic methods for neural network training. Moreover, the basic principles and fundamental ideas given in the book will allow the readers to create successful training methods on their own. Apart from Chapter 1, which reviews classical training methods, the chapters are divided into three main categories. The first one is devoted to local search based methods, including Simulated Annealing, Tabu Search, and Variable Neighborhood Search. The second part of the book presents population based methods, such as Estimation Distribution algorithms, Scatter Search, and Genetic Algorithms. The third part covers other advanced techniques, such as Ant Colony Optimization, Co-evolutionary methods, GRASP, and Memetic algorithms. Overall, the book's objective is engineered to provide a broad coverage of the concepts, methods, and tools of this important area of ANNs within the realm of continuous optimization.

Continuous System Simulation

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Continuous System Simulation

Continuous System Simulation by François E. Cellier , Ernesto Kofman
English | PDF | 2006 | 659 Pages | ISBN : 0387261028 | 4.8 MB

Continuous System Simulation describes systematically and methodically how mathematical models of dynamic systems, usually described by sets of either ordinary or partial differential equations possibly coupled with algebraic equations, can be simulated on a digital computer.

Large Eddy Simulation of Turbulent Incompressible Flows: Analytical and Numerical Results for a Class of LES Models

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Large Eddy Simulation of Turbulent Incompressible Flows: Analytical and Numerical Results for a Class of LES Models

Large Eddy Simulation of Turbulent Incompressible Flows: Analytical and Numerical Results for a Class of LES Models by Volker John
English | PDF (True) | 2004 | 270 Pages | ISBN : 3540406433 | 19.6 MB

Large eddy simulation (LES) seeks to simulate the large structures of a turbulent flow. This is the first monograph which considers LES from a mathematical point of view. It concentrates on LES models for which mathematical and numerical analysis is already available and on related LES models. Most of the available analysis is given in detail, the implementation of the LES models into a finite element code is described, the efficient solution of the discrete systems is discussed and numerical studies with the considered LES models are presented.

Numerical Methods in Sensitivity Analysis and Shape Optimization

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Numerical Methods in Sensitivity Analysis and Shape Optimization

Numerical Methods in Sensitivity Analysis and Shape Optimization by Emmanuel Laporte , Patrick Tallec
English | PDF | 2003 | 202 Pages | ISBN : 0817643222 | 12.3 MB

Sensitivity analysis and optimal shape design are key issues in engineering that have been affected by advances in numerical tools currently available. This book, and its supplementary online files, presents basic optimization techniques that can be used to compute the sensitivity of a given design to local change, or to improve its performance by local optimization of these data. The relevance and scope of these techniques have improved dramatically in recent years because of progress in discretization strategies, optimization algorithms, automatic differentiation, software availability, and the power of personal computers.

Advances in Gabor Analysis

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Advances in Gabor Analysis

Advances in Gabor Analysis by Hans G. Feichtinger, Thomas Strohmer
English | PDF | 2003 | 369 Pages | ISBN : 0817642390 | 30.1 MB

The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scientific communities with significant developments in harmonic analysis, ranging from abstract har­ monic analysis to basic applications. The title of the series reflects the im­ portance of applications and numerical implementation, but richness and relevance of applications and implementation depend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the interleaving of theory and applications and their creative symbi­ otic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has flour­ ished, developed, and deepened over time within many disciplines and by means of creative cross-fertilization with diverse areas. The intricate and fundamental relationship between harmonic analysis and fields such as sig­ nal processing, partial differential equations (PDEs), and image processing is reflected in our state of the art ANHA series. Our vision of modern harmonic analysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, time­ frequency analysis, and fractal geometry, as well as the diverse topics that impinge on them.

Numerical Modeling in Materials Science and Engineering

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Numerical Modeling in Materials Science and Engineering

Numerical Modeling in Materials Science and Engineering by Michel Rappaz , Michel Bellet , Michel Deville
English | PDF | 2003 | 543 Pages | ISBN : 3540426760 | 65.3 MB

This book introduces the concepts and methodologies related to the modelling of the complex phenomena occurring in materials processing. After a short reminder of conservation laws and constitutive relationships, the authors introduce the main numerical methods: finite differences, finite volumes and finite elements. These techniques are developed in three main chapters of the book that tackle more specific problems: phase transformation, solid mechanics and fluid flow. The two last chapters treat inverse methods to obtain the boundary conditions or the material properties and stochastic methods for microstructural simulation. This book is intended for undergraduate and graduate students in materials science and engineering, mechanical engineering and physics and for engineering professionals or researchers who want to get acquainted with numerical simulation to model and compute materials processing.

Modelling in Natural Sciences: Design, Validation and Case Studies

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Modelling in Natural Sciences: Design, Validation and Case Studies

Modelling in Natural Sciences: Design, Validation and Case Studies by Tibor Müller , Harmund Müller
English | PDF | 2003 | 469 Pages | ISBN : 3540001530 | 43.5 MB

This book defines the wide application of the art of modelling. The main emphasis is on the imaging of dynamic processes which are analysed and subdivided into their atomic constituents by means of systems analysis. The cyclic structure and the stages of models set-up are explained. The evaluation of a models quality is regarded as a stochastic process. The aspects of grade used in different fields of sciences are brought into perspective. Thus, a quantitative concept of validity on the basis of conditional degrees of rational belief can be developed.

Complementarity, Equilibrium, Efficiency and Economics

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Complementarity, Equilibrium, Efficiency and Economics

Complementarity, Equilibrium, Efficiency and Economics by G. Isac , V. A. Bulavsky , V. V. Kalashnikov
English | PDF | 2002 | 458 Pages | ISBN : 1402006888 | 38.1 MB

In complementarity theory, which is a relatively new domain of applied mathematics, several kinds of mathematical models and problems related to the study of equilibrium are considered from the point of view of physics as well as economics. In this book the authors have combined complementarity theory, equilibrium of economical systems, and efficiency in Pareto's sense. The authors discuss the use of complementarity theory in the study of equilibrium of economic systems and present results they have obtained. In addition the authors present several new results in complementarity theory and several numerical methods for solving complementarity problems associated with the study of economic equilibrium. The most important notions of Pareto efficiency are also presented.

Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming

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Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming

Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications by Mohit Tawarmalani , Nikolaos V. Sahinidis
English | PDF | 2002 | 492 Pages | ISBN : 1402010311 | 32.8 MB

Interest in constrained optimization originated with the simple linear pro­ gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models.

Kinetic Theory and Fluid Dynamics

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Kinetic Theory and Fluid Dynamics

Kinetic Theory and Fluid Dynamics by Yoshio Sone
English | PDF EPUB (True) | 2002 | 358 Pages | ISBN : 0817642846 | 30.2 MB

This monograph is intended to provide a comprehensive description of the rela­ tion between kinetic theory and fluid dynamics for a time-independent behavior of a gas in a general domain. A gas in a steady (or time-independent) state in a general domain is considered, and its asymptotic behavior for small Knudsen numbers is studied on the basis of kinetic theory. Fluid-dynamic-type equations and their associated boundary conditions, together with their Knudsen-layer corrections, describing the asymptotic behavior of the gas for small Knudsen numbers are presented.

Computational Physiology: Simula Summer School 2023 − Student Reports

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Computational Physiology: Simula Summer School 2023 − Student Reports

Computational Physiology: Simula Summer School 2023 − Student Reports by Kimberly J. McCabe
English | PDF (True) | 2024 | 120 Pages | ISBN : 3031531442 | 8.9 MB

This volume compiles student reports from the 2023 Simula Summer School in Computational Physiology. The reports provide an overview of some tools available to model physiology in excitable tissues across scales and scientific questions.

Dynamical Systems with Applications using MAPLE

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Dynamical Systems with Applications using MAPLE

Dynamical Systems with Applications using MAPLE by Stephen Lynch
English | PDF | 2001 | 400 Pages | ISBN : 0817641505 | 27.9 MB

This book provides an introduction to the theory of dynamical systems with the aid of the Maple algebraic manipulation package. lt is written for both senior un­ dergraduates and first-year graduale students. The firsthalf of the book deals with continuous systems using ordinary differential equations (Chapters 1-12) and the second half is devoted to the study of discrete dynamical systems (Chapters 13-20). (The author has gone for breadth of coverage rather than fine detail and theorems with proof are kept at a minimum.) The material is not clouded by functional analytic and group theoretical definitions, and so is intelligible to readers with a general mathematical background. Some of the topics covered are scarcely cov­ ered elsewhere. Most of the material in Chapters 9-12, 16, 17, 19, and 20 is at postgraduale Ievel and has been influenced by the author's own research interests. It has been found that these chapters are especially useful as reference material for senior undergraduate project work. The book has a very hands-on approach and takes the reader from the basic theory right through to recently published research material.