Mathematical Modelling Optimization Analytic And Numerical Solutions

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Mathematical Modelling, Optimization, Analytic and Numerical Solutions

Pammy Manchanda,René Pierre Lozi,Abul Hasan Siddiqi
Mathematical Modelling Optimization Analytic and Numerical Solutions Book PDF

Author : Pammy Manchanda,René Pierre Lozi,Abul Hasan Siddiqi
Publisher : Springer Nature
Page : 431 pages
File Size : 52,8 Mb
Release : 2020-02-04
Category : Mathematics
ISBN : 9789811509285

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Mathematical Modelling, Optimization, Analytic and Numerical Solutions by Pammy Manchanda,René Pierre Lozi,Abul Hasan Siddiqi Pdf

This book discusses a variety of topics related to industrial and applied mathematics, focusing on wavelet theory, sampling theorems, inverse problems and their applications, partial differential equations as a model of real-world problems, computational linguistics, mathematical models and methods for meteorology, earth systems, environmental and medical science, and the oil industry. It features papers presented at the International Conference in Conjunction with 14th Biennial Conference of ISIAM, held at Guru Nanak Dev University, Amritsar, India, on 2–4 February 2018. The conference has emerged as an influential forum, bringing together prominent academic scientists, experts from industry, and researchers. The topics discussed include Schrodinger operators, quantum kinetic equations and their application, extensions of fractional integral transforms, electrical impedance tomography, diffuse optical tomography, Galerkin method by using wavelets, a Cauchy problem associated with Korteweg–de Vries equation, and entropy solution for scalar conservation laws. This book motivates and inspires young researchers in the fields of industrial and applied mathematics.

Numerical Analysis and Optimization

Grégoire Allaire
Numerical Analysis and Optimization Book PDF

Author : Grégoire Allaire
Publisher : Unknown
Page : 0 pages
File Size : 53,6 Mb
Release : 2023
Category : Mathematical models
ISBN : 1383034443

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Numerical Analysis and Optimization by Grégoire Allaire Pdf

This work familiarises students with mathematical models (PDEs) and methods of numerical solution and optimisation. Including numerous exercises and examples, this is an ideal text for advanced students in Applied Mathematics, Engineering, Physical Science and Computer Science.

Mathematical Modeling with Multidisciplinary Applications

Xin-She Yang
Mathematical Modeling with Multidisciplinary Applications Book PDF

Author : Xin-She Yang
Publisher : John Wiley & Sons
Page : 592 pages
File Size : 51,8 Mb
Release : 2013-04-01
Category : Mathematics
ISBN : 9781118458624

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Mathematical Modeling with Multidisciplinary Applications by Xin-She Yang Pdf

Features mathematical modeling techniques and real-world processes with applications in diverse fields Mathematical Modeling with Multidisciplinary Applications details the interdisciplinary nature of mathematical modeling and numerical algorithms. The book combines a variety of applications from diverse fields to illustrate how the methods can be used to model physical processes, design new products, find solutions to challenging problems, and increase competitiveness in international markets. Written by leading scholars and international experts in the field, the book presents new and emerging topics in areas including finance and economics, theoretical and applied mathematics, engineering and machine learning, physics, chemistry, ecology, and social science. In addition, the book thoroughly summarizes widely used mathematical and numerical methods in mathematical modeling and features: Diverse topics such as partial differential equations (PDEs), fractional calculus, inverse problems by ordinary differential equations (ODEs), semigroups, decision theory, risk analysis, Bayesian estimation, nonlinear PDEs in financial engineering, perturbation analysis, and dynamic system modeling Case studies and real-world applications that are widely used for current mathematical modeling courses, such as the green house effect and Stokes flow estimation Comprehensive coverage of a wide range of contemporary topics, such as game theory, statistical models, and analytical solutions to numerical methods Examples, exercises with select solutions, and detailed references to the latest literature to solidify comprehensive learning New techniques and applications with balanced coverage of PDEs, discrete models, statistics, fractional calculus, and more Mathematical Modeling with Multidisciplinary Applications is an excellent book for courses on mathematical modeling and applied mathematics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for research scientists, mathematicians, and engineers who would like to develop further insights into essential mathematical tools.

Numerical Methods in Sensitivity Analysis and Shape Optimization

Emmanuel Laporte,Patrick Le Tallec
Numerical Methods in Sensitivity Analysis and Shape Optimization Book PDF

Author : Emmanuel Laporte,Patrick Le Tallec
Publisher : Springer Science & Business Media
Page : 202 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461200697

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Numerical Methods in Sensitivity Analysis and Shape Optimization by Emmanuel Laporte,Patrick Le Tallec Pdf

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. Numerical Methods in Sensitivity Analysis and Shape Optimization will be of interest to graduate students involved in mathematical modeling and simulation, as well as engineers and researchers in applied mathematics looking for an up-to-date introduction to optimization techniques, sensitivity analysis, and optimal design.

The Nature of Mathematical Modeling

Neil A. Gershenfeld
The Nature of Mathematical Modeling Book PDF

Author : Neil A. Gershenfeld
Publisher : Cambridge University Press
Page : 268 pages
File Size : 51,7 Mb
Release : 1999
Category : Science
ISBN : 0521570956

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The Nature of Mathematical Modeling by Neil A. Gershenfeld Pdf

This is a book about the nature of mathematical modeling, and about the kinds of techniques that are useful for modeling. The text is in four sections. The first covers exact and approximate analytical techniques; the second, numerical methods; the third, model inference based on observations; and the last, the special role of time in modeling. Each of the topics in the book would be the worthy subject of a dedicated text, but only by presenting the material in this way is it possible to make so much material accessible to so many people. Each chapter presents a concise summary of the core results in an area. The text is complemented by extensive worked problems.

Modeling, Simulation and Optimization for Science and Technology

William Fitzgibbon,Yuri A. Kuznetsov,Pekka Neittaanmäki,Olivier Pironneau
Modeling Simulation and Optimization for Science and Technology Book PDF

Author : William Fitzgibbon,Yuri A. Kuznetsov,Pekka Neittaanmäki,Olivier Pironneau
Publisher : Springer
Page : 248 pages
File Size : 45,9 Mb
Release : 2014-06-18
Category : Technology & Engineering
ISBN : 9789401790543

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Modeling, Simulation and Optimization for Science and Technology by William Fitzgibbon,Yuri A. Kuznetsov,Pekka Neittaanmäki,Olivier Pironneau Pdf

This volume contains thirteen articles on advances in applied mathematics and computing methods for engineering problems. Six papers are on optimization methods and algorithms with emphasis on problems with multiple criteria; four articles are on numerical methods for applied problems modeled with nonlinear PDEs; two contributions are on abstract estimates for error analysis; finally one paper deals with rare events in the context of uncertainty quantification. Applications include aerospace, glaciology and nonlinear elasticity. Herein is a selection of contributions from speakers at two conferences on applied mathematics held in June 2012 at the University of Jyväskylä, Finland. The first conference, “Optimization and PDEs with Industrial Applications” celebrated the seventieth birthday of Professor Jacques Périaux of the University of Jyväskylä and Polytechnic University of Catalonia (Barcelona Tech) and the second conference, “Optimization and PDEs with Applications” celebrated the seventy-fifth birthday of Professor Roland Glowinski of the University of Houston. This work should be of interest to researchers and practitioners as well as advanced students or engineers in computational and applied mathematics or mechanics.

Methods of Mathematical Modelling

Thomas Witelski,Mark Bowen
Methods of Mathematical Modelling Book PDF

Author : Thomas Witelski,Mark Bowen
Publisher : Springer
Page : 305 pages
File Size : 51,7 Mb
Release : 2015-09-18
Category : Mathematics
ISBN : 9783319230429

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Methods of Mathematical Modelling by Thomas Witelski,Mark Bowen Pdf

This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.

Optimization with PDE Constraints

Michael Hinze,Rene Pinnau,Michael Ulbrich,Stefan Ulbrich
Optimization with PDE Constraints Book PDF

Author : Michael Hinze,Rene Pinnau,Michael Ulbrich,Stefan Ulbrich
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 48,9 Mb
Release : 2008-10-16
Category : Mathematics
ISBN : 9781402088391

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Optimization with PDE Constraints by Michael Hinze,Rene Pinnau,Michael Ulbrich,Stefan Ulbrich Pdf

Solving optimization problems subject to constraints given in terms of partial d- ferential equations (PDEs) with additional constraints on the controls and/or states is one of the most challenging problems in the context of industrial, medical and economical applications, where the transition from model-based numerical si- lations to model-based design and optimal control is crucial. For the treatment of such optimization problems the interaction of optimization techniques and num- ical simulation plays a central role. After proper discretization, the number of op- 3 10 timization variables varies between 10 and 10 . It is only very recently that the enormous advances in computing power have made it possible to attack problems of this size. However, in order to accomplish this task it is crucial to utilize and f- ther explore the speci?c mathematical structure of optimization problems with PDE constraints, and to develop new mathematical approaches concerning mathematical analysis, structure exploiting algorithms, and discretization, with a special focus on prototype applications. The present book provides a modern introduction to the rapidly developing ma- ematical ?eld of optimization with PDE constraints. The ?rst chapter introduces to the analytical background and optimality theory for optimization problems with PDEs. Optimization problems with PDE-constraints are posed in in?nite dim- sional spaces. Therefore, functional analytic techniques, function space theory, as well as existence- and uniqueness results for the underlying PDE are essential to study the existence of optimal solutions and to derive optimality conditions.

Mathematical Modeling and Optimization of Complex Structures

Pekka Neittaanmäki,Sergey Repin,Tero Tuovinen
Mathematical Modeling and Optimization of Complex Structures Book PDF

Author : Pekka Neittaanmäki,Sergey Repin,Tero Tuovinen
Publisher : Springer
Page : 328 pages
File Size : 41,7 Mb
Release : 2015-10-07
Category : Technology & Engineering
ISBN : 9783319235646

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Mathematical Modeling and Optimization of Complex Structures by Pekka Neittaanmäki,Sergey Repin,Tero Tuovinen Pdf

This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented on the International Conference for Mathematical Modeling and Optimization in Mechanics, held in Jyväskylä, Finland, March 6-7, 2014 dedicated to Prof. N. Banichuk on the occasion of his 70th birthday. The articles are written by well-known scientists working in computational mechanics and in optimization of complicated technical models. Also, the volume contains papers discussing the historical development, the state of the art, new ideas, and open problems arising in modern continuum mechanics and applied optimization problems. Several papers are concerned with mathematical problems in numerical analysis, which are also closely related to important mechanical models. The main topics treated include: * Computer simulation methods in mechanics, physics, and biology; * Variational problems and methods; minimization algorithms; * Optimal control problems with distributed and discrete control; * Shape optimization and shape design problems in science and engineering; * Sensitivity analysis and parameters optimization of complex systems.

Matrix, Numerical, and Optimization Methods in Science and Engineering

Kevin W. Cassel
Matrix Numerical and Optimization Methods in Science and Engineering Book PDF

Author : Kevin W. Cassel
Publisher : Cambridge University Press
Page : 727 pages
File Size : 45,8 Mb
Release : 2021-03-04
Category : Mathematics
ISBN : 9781108479097

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Matrix, Numerical, and Optimization Methods in Science and Engineering by Kevin W. Cassel Pdf

Vector and matrix algebra -- Algebraic eigenproblems and their applications -- Differential eigenproblems and their applications -- Vector and matrix calculus -- Analysis of discrete dynamical systems -- Computational linear algebra -- Numerical methods for differential equations -- Finite-difference methods for boundary-value problems -- Finite-difference methods for initial-value problems -- Least-squares methods -- Data analysis : curve fitting and interpolation -- Optimization and root finding of algebraic systems -- Data-driven methods and reduced-order modeling.

Mathematical and Computational Modeling

Roderick Melnik
Mathematical and Computational Modeling Book PDF

Author : Roderick Melnik
Publisher : John Wiley & Sons
Page : 336 pages
File Size : 50,5 Mb
Release : 2015-04-30
Category : Mathematics
ISBN : 9781118854112

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Mathematical and Computational Modeling by Roderick Melnik Pdf

Illustrates the application of mathematical and computational modeling in a variety of disciplines With an emphasis on the interdisciplinary nature of mathematical and computational modeling, Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts features chapters written by well-known, international experts in these fields and presents readers with a host of state-of-the-art achievements in the development of mathematical modeling and computational experiment methodology. The book is a valuable guide to the methods, ideas, and tools of applied and computational mathematics as they apply to other disciplines such as the natural and social sciences, engineering, and technology. Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts also features: Rigorous mathematical procedures and applications as the driving force behind mathematical innovation and discovery Numerous examples from a wide range of disciplines to emphasize the multidisciplinary application and universality of applied mathematics and mathematical modeling Original results on both fundamental theoretical and applied developments in diverse areas of human knowledge Discussions that promote interdisciplinary interactions between mathematicians, scientists, and engineers Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts is an ideal resource for professionals in various areas of mathematical and statistical sciences, modeling and simulation, physics, computer science, engineering, biology and chemistry, industrial, and computational engineering. The book also serves as an excellent textbook for graduate courses in mathematical modeling, applied mathematics, numerical methods, operations research, and optimization.

Mathematical Modelling and Optimization of Engineering Problems

J. A. Tenreiro Machado,Necati Özdemir,Dumitru Baleanu
Mathematical Modelling and Optimization of Engineering Problems Book PDF

Author : J. A. Tenreiro Machado,Necati Özdemir,Dumitru Baleanu
Publisher : Springer Nature
Page : 204 pages
File Size : 54,6 Mb
Release : 2020-02-12
Category : Mathematics
ISBN : 9783030370626

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Mathematical Modelling and Optimization of Engineering Problems by J. A. Tenreiro Machado,Necati Özdemir,Dumitru Baleanu Pdf

This book presents recent developments in modelling and optimization of engineering systems and the use of advanced mathematical methods for solving complex real-world problems. It provides recent theoretical developments and new techniques based on control, optimization theory, mathematical modeling and fractional calculus that can be used to model and understand complex behavior in natural phenomena including latest technologies such as additive manufacturing. Specific topics covered in detail include combinatorial optimization, flow and heat transfer, mathematical modelling, energy storage and management policy, artificial intelligence, optimal control, modelling and optimization of manufacturing systems.

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 : 54,8 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.

Optimization

Jan Brinkhuis,Vladimir Tikhomirov
Optimization Book PDF

Author : Jan Brinkhuis,Vladimir Tikhomirov
Publisher : Princeton University Press
Page : 685 pages
File Size : 44,5 Mb
Release : 2005-09-18
Category : Computers
ISBN : 9780691102870

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Optimization by Jan Brinkhuis,Vladimir Tikhomirov Pdf

This self-contained textbook is an informal introduction to optimization through the use of numerous illustrations and applications. The focus is on analytically solving optimization problems with a finite number of continuous variables. In addition, the authors provide introductions to classical and modern numerical methods of optimization and to dynamic optimization. The book's overarching point is that most problems may be solved by the direct application of the theorems of Fermat, Lagrange, and Weierstrass. The authors show how the intuition for each of the theoretical results can be supported by simple geometric figures. They include numerous applications through the use of varied classical and practical problems. Even experts may find some of these applications truly surprising. A basic mathematical knowledge is sufficient to understand the topics covered in this book. More advanced readers, even experts, will be surprised to see how all main results can be grounded on the Fermat-Lagrange theorem. The book can be used for courses on continuous optimization, from introductory to advanced, for any field for which optimization is relevant.

Analysis, Modelling, Optimization, and Numerical Techniques

Gerard Olivar Tost,Olga Vasilieva
Analysis Modelling Optimization and Numerical Techniques Book PDF

Author : Gerard Olivar Tost,Olga Vasilieva
Publisher : Springer
Page : 371 pages
File Size : 40,5 Mb
Release : 2015-03-18
Category : Mathematics
ISBN : 9783319125831

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Analysis, Modelling, Optimization, and Numerical Techniques by Gerard Olivar Tost,Olga Vasilieva Pdf

This book highlights recent compelling research results and trends in various aspects of contemporary mathematics, emphasizing applicabilitions to real-world situations. The chapters present exciting new findings and developments in situations where mathematical rigor is combined with common sense. A multi-disciplinary approach, both within each chapter and in the volume as a whole, leads to practical insights that may result in a more synthetic understanding of specific global issues as well as their possible solutions. The volume will be of interest not only to experts in mathematics, but also to graduate students, scientists, and practitioners from other fields including physics, biology, geology, management, and medicine.