Numerical Analysis and Optimization

Numerical Analysis and Optimization PDF

Author: Grégoire Allaire

Publisher: OUP Oxford

Published: 2007-05-24

Total Pages: 472

ISBN-13: 0191525529

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This text, based on the author's teaching at École Polytechnique, introduces the reader to the world of mathematical modelling and numerical simulation. Covering the finite difference method; variational formulation of elliptic problems; Sobolev spaces; elliptical problems; the finite element method; Eigenvalue problems; evolution problems; optimality conditions and algorithms and methods of operational research, and including a several exercises throughout, this is an ideal text for advanced undergraduate students and graduates in applied mathematics, engineering, computer science, and the physical sciences.

Numerical Methods and Analysis with Mathematical Modelling

Numerical Methods and Analysis with Mathematical Modelling PDF

Author: William P. Fox

Publisher: CRC Press

Published: 2024-08-07

Total Pages: 424

ISBN-13: 1040098134

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What sets Numerical Methods and Analysis with Mathematical Modelling apart are the modelling aspects utilizing numerical analysis (methods) to obtain solutions. The authors cover first the basic numerical analysis methods with simple examples to illustrate the techniques and discuss possible errors. The modelling prospective reveals the practical relevance of the numerical methods in context to real-world problems. At the core of this text are the real-world modelling projects. Chapters are introduced and techniques are discussed with common examples. A modelling scenario is introduced that will be solved with these techniques later in the chapter. Often, the modelling problems require more than one previously covered technique presented in the book. Fundamental exercises to practice the techniques are included. Multiple modelling scenarios per numerical methods illustrate the applications of the techniques introduced. Each chapter has several modelling examples that are solved by the methods described within the chapter. The use of technology is instrumental in numerical analysis and numerical methods. In this text, Maple, Excel, R, and Python are illustrated. The goal is not to teach technology but to illustrate its power and limitations to perform algorithms and reach conclusions. This book fulfills a need in the education of all students who plan to use technology to solve problems whether using physical models or true creative mathematical modeling, like discrete dynamical systems.

Mathematical Modelling and Numerical Methods in Finance

Mathematical Modelling and Numerical Methods in Finance PDF

Author: Alain Bensoussan

Publisher: Elsevier

Published: 2009-06-16

Total Pages: 743

ISBN-13: 0080931006

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Mathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains. Coverage of all aspects of quantitative finance including models, computational methods and applications Provides an overview of new ideas and results Contributors are leaders of the field

Numerical Analysis and Optimization

Numerical Analysis and Optimization PDF

Author: Grégoire Allaire

Publisher: Oxford University Press

Published: 2007-05-24

Total Pages: 472

ISBN-13: 0199205213

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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.

The Nature of Mathematical Modeling

The Nature of Mathematical Modeling PDF

Author: Neil A. Gershenfeld

Publisher: Cambridge University Press

Published: 1999

Total Pages: 268

ISBN-13: 9780521570954

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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.

Mathematical Modeling and Numerical Methods in Chemical Physics and Mechanics

Mathematical Modeling and Numerical Methods in Chemical Physics and Mechanics PDF

Author: Ali V. Aliev

Publisher: CRC Press

Published: 2016-04-27

Total Pages: 410

ISBN-13: 1771882905

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The use of mathematical modeling in engineering allows for a significant reduction of material costs associated with design, production, and operation of technical objects, but it is important for an engineer to use the available computational approaches in modeling correctly. Taking into account the level of modern computer technology, this new volume explains how an engineer should properly define the physical and mathematical problem statement, choose the computational approach, and solve the problem by proven reliable computational approach using computer and software applications during the solution of a particular problem. This work is the result of years of the authors’ research and experience in the fields of power and rocket engineering where they put into practice the methods of mathematical modeling shown in this valuable volume. The examples in the book are based on two approaches. The first approach involves the use of the relatively simple mathematical system MathCad. The second one involves the solving of problems using Intel Visual Fortran compiler with IMSL Libraries. The use of other software packages (Maple, MathLab, Mathematica) or compilers (С, С++, Visual Basic) for code is equally acceptable in the solution of the problems given in the book. Intended for professors and instructors, scientific researchers, students, and industry professionals, the book will help readers to choose the most appropriate mathematical modeling method to solve engineering problems, and the authors also include methods that allow for the solving of nonmathematical problems as mathematical problems.

Mathematical and Numerical Modeling in Porous Media

Mathematical and Numerical Modeling in Porous Media PDF

Author: Martin A. Diaz Viera

Publisher: CRC Press

Published: 2012-07-24

Total Pages: 370

ISBN-13: 0203113888

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Porous media are broadly found in nature and their study is of high relevance in our present lives. In geosciences porous media research is fundamental in applications to aquifers, mineral mines, contaminant transport, soil remediation, waste storage, oil recovery and geothermal energy deposits. Despite their importance, there is as yet no complete

Advanced Numerical Methods for Differential Equations

Advanced Numerical Methods for Differential Equations PDF

Author: Harendra Singh

Publisher: CRC Press

Published: 2021-07-29

Total Pages: 336

ISBN-13: 1000381080

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Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.

A Primer on Mathematical Modelling

A Primer on Mathematical Modelling PDF

Author: Alfio Quarteroni

Publisher: Springer Nature

Published: 2020-10-09

Total Pages: 238

ISBN-13: 3030445410

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In this book we describe the magic world of mathematical models: starting from real-life problems, we formulate them in terms of equations, transform equations into algorithms and algorithms into programs to be executed on computers. A broad variety of examples and exercises illustrate that properly designed models can, e.g.: predict the way the number of dolphins in the Aeolian Sea will change as food availability and fishing activity vary; describe the blood flow in a capillary network; calculate the PageRank of websites. This book also includes a chapter with an elementary introduction to Octave, an open-source programming language widely used in the scientific community. Octave functions and scripts for dealing with the problems presented in the text can be downloaded from https://paola-gervasio.unibs.it/quarteroni-gervasio This book is addressed to any student interested in learning how to construct and apply mathematical models.

Numerical Methods in Finance

Numerical Methods in Finance PDF

Author: L. C. G. Rogers

Publisher: Cambridge University Press

Published: 1997-06-26

Total Pages: 348

ISBN-13: 9780521573542

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Numerical Methods in Finance describes a wide variety of numerical methods used in financial analysis.