Differential Equations Mathematical Modeling And Computational Algorithms

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Differential Equations, Mathematical Modeling and Computational Algorithms

Vladimir Vasilyev
Differential Equations Mathematical Modeling and Computational Algorithms Book PDF

Author : Vladimir Vasilyev
Publisher : Springer Nature
Page : 294 pages
File Size : 55,6 Mb
Release : 2023-06-06
Category : Mathematics
ISBN : 9783031285059

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Differential Equations, Mathematical Modeling and Computational Algorithms by Vladimir Vasilyev Pdf

This book contains reports made at the International Conference on Differential Equations, Mathematical Modeling and Computational Algorithms, held in Belgorod, Russia, in October 2021 and is devoted to various aspects of the theory of differential equations and their applications in various branches of science. Theoretical papers devoted to the qualitative analysis of emerging mathematical objects, theorems of the existence and uniqueness of solutions to the boundary value problems under study are presented, and numerical algorithms for their solution are described. Some issues of mathematical modeling are also covered; in particular, in problems of economics, computational aspects of the theory of differential equations and boundary value problems are studied. The articles are written by well-known experts and are interesting and useful to a wide audience: mathematicians, representatives of applied sciences and students and postgraduates of universities engaged in applied mathematics.

Differential Equations, Mathematical Modeling and Computational Algorithms

Vladimir Vasilyev
Differential Equations Mathematical Modeling and Computational Algorithms Book PDF

Author : Vladimir Vasilyev
Publisher : Unknown
Page : 0 pages
File Size : 42,7 Mb
Release : 2023
Category : Electronic
ISBN : 3031285077

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Differential Equations, Mathematical Modeling and Computational Algorithms by Vladimir Vasilyev Pdf

This book contains reports made at the International Conference on Differential Equations, Mathematical Modeling and Computational Algorithms, held in Belgorod, Russia, in October 2021 and is devoted to various aspects of the theory of differential equations and their applications in various branches of science. Theoretical papers devoted to the qualitative analysis of emerging mathematical objects, theorems of the existence and uniqueness of solutions to the boundary value problems under study are presented, and numerical algorithms for their solution are described. Some issues of mathematical modeling are also covered; in particular, in problems of economics, computational aspects of the theory of differential equations and boundary value problems are studied. The articles are written by well-known experts and are interesting and useful to a wide audience: mathematicians, representatives of applied sciences and students and postgraduates of universities engaged in applied mathematics.

Differential Equations, Mathematical Modeling and Computational Algorithms

Vladimir Vasilyev
Differential Equations Mathematical Modeling and Computational Algorithms Book PDF

Author : Vladimir Vasilyev
Publisher : Unknown
Page : 0 pages
File Size : 51,8 Mb
Release : 2023
Category : Electronic
ISBN : 3031285069

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Differential Equations, Mathematical Modeling and Computational Algorithms by Vladimir Vasilyev Pdf

This book contains reports made at the International Conference on Differential Equations, Mathematical Modeling and Computational Algorithms, held in Belgorod, Russia, in October 2021 and is devoted to various aspects of the theory of differential equations and their applications in various branches of science. Theoretical papers devoted to the qualitative analysis of emerging mathematical objects, theorems of the existence and uniqueness of solutions to the boundary value problems under study are presented, and numerical algorithms for their solution are described. Some issues of mathematical modeling are also covered; in particular, in problems of economics, computational aspects of the theory of differential equations and boundary value problems are studied. The articles are written by well-known experts and are interesting and useful to a wide audience: mathematicians, representatives of applied sciences and students and postgraduates of universities engaged in applied mathematics.

Modelling with Ordinary Differential Equations

T.P. Dreyer
Modelling with Ordinary Differential Equations Book PDF

Author : T.P. Dreyer
Publisher : CRC Press
Page : 302 pages
File Size : 46,9 Mb
Release : 1993-06-28
Category : Mathematics
ISBN : 0849386365

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Modelling with Ordinary Differential Equations by T.P. Dreyer Pdf

Modelling with Ordinary Differential Equations integrates standard material from an elementary course on ordinary differential equations with the skills of mathematical modeling in a number of diverse real-world situations. Each situation highlights a different aspect of the theory or modeling. Carefully selected exercises and projects present excellent opportunities for tutorial sessions and self-study. This text/reference addresses common types of first order ordinary differential equations and the basic theory of linear second order equations with constant coefficients. It also explores the elementary theory of systems of differential equations, Laplace transforms, and numerical solutions. Theorems on the existence and uniqueness of solutions are a central feature. Topics such as curve fitting, time-delay equations, and phase plane diagrams are introduced. The book includes algorithms for computer programs as an integral part of the answer-finding process. Professionals and students in the social and biological sciences, as well as those in physics and mathematics will find this text/reference indispensable for self-study.

Computational Mathematical Modeling

Daniela Calvetti,Erkki Somersalo
Computational Mathematical Modeling Book PDF

Author : Daniela Calvetti,Erkki Somersalo
Publisher : SIAM
Page : 234 pages
File Size : 50,7 Mb
Release : 2012-01-01
Category : Differential equations
ISBN : 1611972485

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Computational Mathematical Modeling by Daniela Calvetti,Erkki Somersalo Pdf

Interesting, real-world mathematical modeling problems are complex and can usually be studied at different scales. The scale at which the investigation is carried out is one of the factors that determines the type of mathematics most appropriate to describe the problem. The book concentrates on two modeling paradigms: the macroscopic, in which the authors describe phenomena in terms of time evolution via ordinary differential equations, and the microscopic, which requires knowledge of random events and probability. The text emphasizes the development of computational skills to construct predictive models and analyze the results. To elucidate the concepts, a wealth of examples and portions of MATLAB® code used by the authors are included.

Mathematical Modelling

Seyed M. Moghadas,Majid Jaberi-Douraki
Mathematical Modelling Book PDF

Author : Seyed M. Moghadas,Majid Jaberi-Douraki
Publisher : John Wiley & Sons
Page : 192 pages
File Size : 41,6 Mb
Release : 2018-07-24
Category : Mathematics
ISBN : 9781119483991

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Mathematical Modelling by Seyed M. Moghadas,Majid Jaberi-Douraki Pdf

An important resource that provides an overview of mathematical modelling Mathematical Modelling offers a comprehensive guide to both analytical and computational aspects of mathematical modelling that encompasses a wide range of subjects. The authors provide an overview of the basic concepts of mathematical modelling and review the relevant topics from differential equations and linear algebra. The text explores the various types of mathematical models, and includes a range of examples that help to describe a variety of techniques from dynamical systems theory. The book’s analytical techniques examine compartmental modelling, stability, bifurcation, discretization, and fixed-point analysis. The theoretical analyses involve systems of ordinary differential equations for deterministic models. The text also contains information on concepts of probability and random variables as the requirements of stochastic processes. In addition, the authors describe algorithms for computer simulation of both deterministic and stochastic models, and review a number of well-known models that illustrate their application in different fields of study. This important resource: Includes a broad spectrum of models that fall under deterministic and stochastic classes and discusses them in both continuous and discrete forms Demonstrates the wide spectrum of problems that can be addressed through mathematical modelling based on fundamental tools and techniques in applied mathematics and statistics Contains an appendix that reveals the overall approach that can be taken to solve exercises in different chapters Offers many exercises to help better understand the modelling process Written for graduate students in applied mathematics, instructors, and professionals using mathematical modelling for research and training purposes, Mathematical Modelling: A Graduate Textbook covers a broad range of analytical and computational aspects of mathematical modelling.

Mathematical Modelling

J. Caldwell,Douglas K.S. Ng
Mathematical Modelling Book PDF

Author : J. Caldwell,Douglas K.S. Ng
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 40,9 Mb
Release : 2006-04-10
Category : Mathematics
ISBN : 9781402019937

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Mathematical Modelling by J. Caldwell,Douglas K.S. Ng Pdf

Over the past decade there has been an increasing demand for suitable material in the area of mathematical modelling as applied to science, engineering, business and management. Recent developments in computer technology and related software have provided the necessary tools of increasing power and sophistication which have significant implications for the use and role of mathematical modelling in the above disciplines. In the past, traditional methods have relied heavily on expensive experimentation and the building of scaled models, but now a more flexible and cost effective approach is available through greater use of mathematical modelling and computer simulation. In particular, developments in computer algebra, symbolic manipulation packages and user friendly software packages for large scale problems, all have important implications in both the teaching of mathematical modelling and, more importantly, its use in the solution of real world problems. Many textbooks have been published which cover the art and techniques of modelling as well as specific mathematical modelling techniques in specialist areas within science and business. In most of these books the mathematical material tends to be rather tailor made to fit in with a one or two semester course for teaching students at the undergraduate or postgraduate level, usually the former. This textbook is quite different in that it is intended to build on and enhance students’ modelling skills using a combination of case studies and projects.

Numerical Methods

Anne Greenbaum,Tim P. Chartier
Numerical Methods Book PDF

Author : Anne Greenbaum,Tim P. Chartier
Publisher : Princeton University Press
Page : 471 pages
File Size : 52,7 Mb
Release : 2012-04-01
Category : Mathematics
ISBN : 9781400842674

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Numerical Methods by Anne Greenbaum,Tim P. Chartier Pdf

A rigorous and comprehensive introduction to numerical analysis Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results. The book gives instructors the flexibility to emphasize different aspects—design, analysis, or computer implementation—of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book also includes polynomial interpolation at Chebyshev points, use of the MATLAB package Chebfun, and a section on the fast Fourier transform. Supplementary materials are available online. Clear and concise exposition of standard numerical analysis topics Explores nontraditional topics, such as mathematical modeling and Monte Carlo methods Covers modern applications, including information retrieval and animation, and classical applications from physics and engineering Promotes understanding of computational results through MATLAB exercises Provides flexibility so instructors can emphasize mathematical or applied/computational aspects of numerical methods or a combination Includes recent results on polynomial interpolation at Chebyshev points and use of the MATLAB package Chebfun Short discussions of the history of numerical methods interspersed throughout Supplementary materials available online

Soft Computing Approach for Mathematical Modeling of Engineering Problems

Ali Ahmadian,Soheil Salahshour
Soft Computing Approach for Mathematical Modeling of Engineering Problems Book PDF

Author : Ali Ahmadian,Soheil Salahshour
Publisher : CRC Press
Page : 223 pages
File Size : 44,8 Mb
Release : 2021-09-02
Category : Computers
ISBN : 9781000432442

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Soft Computing Approach for Mathematical Modeling of Engineering Problems by Ali Ahmadian,Soheil Salahshour Pdf

This book describes different mathematical modeling and soft computing techniques used to solve practical engineering problems. It gives an overview of the current state of soft computing techniques and describes the advantages and disadvantages of soft computing compared to traditional hard computing techniques. Through examples and case studies, the editors demonstrate and describe how problems with inherent uncertainty can be addressed and eventually solved through the aid of numerical models and methods. The chapters address several applications and examples in bioengineering science, drug delivery, solving inventory issues, Industry 4.0, augmented reality and weather forecasting. Other examples include solving fuzzy-shortest-path problems by introducing a new distance and ranking functions. Because, in practice, problems arise with uncertain data and most of them cannot be solved exactly and easily, the main objective is to develop models that deliver solutions with the aid of numerical methods. This is the reason behind investigating soft numerical computing in dynamic systems. Having this in mind, the authors and editors have considered error of approximation and have discussed several common types of errors and their propagations. Moreover, they have explained the numerical methods, along with convergence and consistence properties and characteristics, as the main objectives behind this book involve considering, discussing and proving related theorems within the setting of soft computing. This book examines dynamic models, and how time is fundamental to the structure of the model and data as well as the understanding of how a process unfolds • Discusses mathematical modeling with soft computing and the implementations of uncertain mathematical models • Examines how uncertain dynamic systems models include uncertain state, uncertain state space and uncertain state’s transition functions • Assists readers to become familiar with many soft numerical methods to simulate the solution function’s behavior This book is intended for system specialists who are interested in dynamic systems that operate at different time scales. The book can be used by engineering students, researchers and professionals in control and finite element fields as well as all engineering, applied mathematics, economics and computer science interested in dynamic and uncertain systems. Ali Ahmadian is a Senior Lecturer at the Institute of IR 4.0, The National University of Malaysia. Soheil Salahshour is an associate professor at Bahcesehir University.

Partial Differential Equations

R. M. M. Mattheij,S. W. Rienstra,J. H. M. ten Thije Boonkkamp
Partial Differential Equations Book PDF

Author : R. M. M. Mattheij,S. W. Rienstra,J. H. M. ten Thije Boonkkamp
Publisher : SIAM
Page : 697 pages
File Size : 55,8 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 0898718279

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Partial Differential Equations by R. M. M. Mattheij,S. W. Rienstra,J. H. M. ten Thije Boonkkamp Pdf

Partial differential equations (PDEs) are used to describe a large variety of physical phenomena, from fluid flow to electromagnetic fields, and are indispensable to such disparate fields as aircraft simulation and computer graphics. While most existing texts on PDEs deal with either analytical or numerical aspects of PDEs, this innovative and comprehensive textbook features a unique approach that integrates analysis and numerical solution methods and includes a third component - modeling - to address real-life problems. The authors believe that modeling can be learned only by doing; hence a separate chapter containing 16 user-friendly case studies of elliptic, parabolic, and hyperbolic equations is included and numerous exercises are included in all other chapters.

Computational Differential Equations

Kenneth Eriksson
Computational Differential Equations Book PDF

Author : Kenneth Eriksson
Publisher : Cambridge University Press
Page : 558 pages
File Size : 51,8 Mb
Release : 1996-09-05
Category : Mathematics
ISBN : 0521567386

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Computational Differential Equations by Kenneth Eriksson Pdf

This textbook on computational mathematics is based on a fusion of mathematical analysis, numerical computation and applications.

Scientific Computing with Case Studies

Dianne P. O'Leary
Scientific Computing with Case Studies Book PDF

Author : Dianne P. O'Leary
Publisher : SIAM
Page : 377 pages
File Size : 50,9 Mb
Release : 2009-01-01
Category : Mathematics
ISBN : 9780898717723

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Scientific Computing with Case Studies by Dianne P. O'Leary Pdf

This book is a practical guide to the numerical solution of linear and nonlinear equations, differential equations, optimization problems, and eigenvalue problems. It treats standard problems and introduces important variants such as sparse systems, differential-algebraic equations, constrained optimization, Monte Carlo simulations, and parametric studies. Stability and error analysis are emphasized, and the Matlab algorithms are grounded in sound principles of software design and understanding of machine arithmetic and memory management. Nineteen case studies provide experience in mathematical modeling and algorithm design, motivated by problems in physics, engineering, epidemiology, chemistry, and biology. The topics included go well beyond the standard first-course syllabus, introducing important problems such as differential-algebraic equations and conic optimization problems, and important solution techniques such as continuation methods. The case studies cover a wide variety of fascinating applications, from modeling the spread of an epidemic to determining truss configurations.

Mathematical Modeling and Computational Science

Gheorghe Adam,Ján Buša,Michal Hnatič
Mathematical Modeling and Computational Science Book PDF

Author : Gheorghe Adam,Ján Buša,Michal Hnatič
Publisher : Springer
Page : 336 pages
File Size : 55,7 Mb
Release : 2012-02-21
Category : Computers
ISBN : 9783642282126

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Mathematical Modeling and Computational Science by Gheorghe Adam,Ján Buša,Michal Hnatič Pdf

This book constitutes the refereed post-proceedings of the International Conference on Mathematical Modeling and Computational Physics, MMCP 2011, held in Stará Lesná, Slovakia, in July 2011. The 41 revised papers presented were carefully reviewed and selected from numerous submissions. They are organized in topical sections on mathematical modeling and methods, numerical modeling and methods, computational support of the experiments, computing tools, and optimization and simulation.

Large Scale Scientific Computing

Deuflhard
Large Scale Scientific Computing Book PDF

Author : Deuflhard
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468467543

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Large Scale Scientific Computing by Deuflhard Pdf

In this book, the new and rapidly expanding field of scientific computing is understood in a double sense: as computing for scientific and engineering problems and as the science of doing such computations. Thus scientific computing touches at one side mathematical modelling (in the various fields of applications) and at the other side computer science. As soon as the mathematical models de scribe the features of real life processes in sufficient detail, the associated computations tend to be large scale. As a consequence, interest more and more focusses on such numerical methods that can be expected to cope with large scale computational problems. Moreover, given the algorithms which are known to be efficient on a tradi tional computer, the question of implementation on modern supercomputers may get crucial. The present book is the proceedings of a meeting on "Large Scale Scientific Computing" , that was held a t the Oberwolfach Mathematical Institute (July 14-19, 1985) under the auspices of the Sonderforschungsbereich 123 of the University of Heidelberg. Participants included applied scientists with computational interests, numerical analysts, and experts on modern parallel computers. 'l'he purpose of the meeting was to establish a common under standing of recent issues in scientific computing, especially in view of large scale problems. Fields of applications, which have been covered, included semi-conductor design, chemical combustion, flow through porous media, climatology, seismology, fluid dynami. cs, tomography, rheology, hydro power plant optimization, subwil. y control, space technology.

Snapshot-Based Methods and Algorithms

Peter Benner,et al.
Snapshot Based Methods and Algorithms Book PDF

Author : Peter Benner,et al.
Publisher : Walter de Gruyter GmbH & Co KG
Page : 356 pages
File Size : 53,5 Mb
Release : 2020-12-16
Category : Mathematics
ISBN : 9783110671490

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Snapshot-Based Methods and Algorithms by Peter Benner,et al. Pdf

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science.