Computer Methods For Ordinary Differential Equations And Differential Algebraic Equations

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Computer Methods For Ordinary Differential Equations And Differential Algebraic Equations

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Author : Uri M. Ascher
language : en
Publisher: SIAM
Release Date : 1998-01-01

Computer Methods For Ordinary Differential Equations And Differential Algebraic Equations written by Uri M. Ascher and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.

Designed for those people who want to gain a practical knowledge of modern techniques, this book contains all the material necessary for a course on the numerical solution of differential equations. Written by two of the field's leading authorities, it provides a unified presentation of initial value and boundary value problems in ODEs as well as differential-algebraic equations. The approach is aimed at a thorough understanding of the issues and methods for practical computation while avoiding an extensive theorem-proof type of exposition. It also addresses reasons why existing software succeeds or fails. This book is a practical and mathematically well-informed introduction that emphasizes basic methods and theory, issues in the use and development of mathematical software, and examples from scientific engineering applications. Topics requiring an extensive amount of mathematical development, such as symplectic methods for Hamiltonian systems, are introduced, motivated, and included in the exercises, but a complete and rigorous mathematical presentation is referenced rather than included.

Computer Methods For Ordinary Differential Equations And Differential Algebraic Equations

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Author : Uri M. Ascher
language : en
Publisher: SIAM
Release Date : 1998-08-01

Computer Methods For Ordinary Differential Equations And Differential Algebraic Equations written by Uri M. Ascher and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-01 with Mathematics categories.

This book contains all the material necessary for a course on the numerical solution of differential equations.

Fundamentals Of Ordinary Differential Equations

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Author : Mohit Chatterjee
language : en
Publisher: Educohack Press
Release Date : 2025-02-20

Fundamentals Of Ordinary Differential Equations written by Mohit Chatterjee and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.

"Fundamentals of Ordinary Differential Equations" is a comprehensive guide designed for students, researchers, and professionals to master ODE theory and applications. We cover essential principles, advanced techniques, and practical applications, providing a well-rounded resource for understanding differential equations and their real-world impact. The book offers a multifaceted approach, from basic principles to advanced concepts, catering to fields like physics, engineering, biology, and economics. Mathematical ideas are broken down with step-by-step explanations, examples, and illustrations, making complex concepts accessible. Real-world examples throughout each chapter show how ODEs model and analyze systems in diverse disciplines. We also explain numerical methods such as Euler’s method, Runge-Kutta, and finite differences, equipping readers with computational tools for solving ODEs. Advanced topics include bifurcation, chaos theory, Hamiltonian systems, and singular perturbations, providing an in-depth grasp of ODE topics. With chapter summaries, exercises, glossaries, and additional resources, "Fundamentals of Ordinary Differential Equations" is an essential reference for students, professionals, and practitioners across science and engineering fields.

Solving Differential Equations In R

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Author : Karline Soetaert
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-06

Solving Differential Equations In R written by Karline Soetaert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-06 with Computers categories.

Mathematics plays an important role in many scientific and engineering disciplines. This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. It is therefore intended for the practitioner, the student and the scientist, who wants to know how to use R for solving differential equations. However, it has been our goal that non-mathematicians should at least understand the basics of the methods, while obtaining entrance into the relevant literature that provides more mathematical background. Therefore, each chapter that deals with R examples is preceded by a chapter where the theory behind the numerical methods being used is introduced. In the sections that deal with the use of R for solving differential equations, we have taken examples from a variety of disciplines, including biology, chemistry, physics, pharmacokinetics. Many examples are well-known test examples, used frequently in the field of numerical analysis.

Simulation Of Ode Pde Models With Matlab Octave And Scilab

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Author : Alain Vande Wouwer
language : en
Publisher: Springer
Release Date : 2014-06-07

Simulation Of Ode Pde Models With Matlab Octave And Scilab written by Alain Vande Wouwer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-07 with Technology & Engineering categories.

Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB shows the reader how to exploit a fuller array of numerical methods for the analysis of complex scientific and engineering systems than is conventionally employed. The book is dedicated to numerical simulation of distributed parameter systems described by mixed systems of algebraic equations, ordinary differential equations (ODEs) and partial differential equations (PDEs). Special attention is paid to the numerical method of lines (MOL), a popular approach to the solution of time-dependent PDEs, which proceeds in two basic steps: spatial discretization and time integration. Besides conventional finite-difference and element techniques, more advanced spatial-approximation methods are examined in some detail, including nonoscillatory schemes and adaptive-grid approaches. A MOL toolbox has been developed within MATLAB®/OCTAVE/SCILAB. In addition to a set of spatial approximations and time integrators, this toolbox includes a collection of application examples, in specific areas, which can serve as templates for developing new programs. Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB provides a practical introduction to some advanced computational techniques for dynamic system simulation, supported by many worked examples in the text, and a collection of codes available for download from the book’s page at www.springer.com. This text is suitable for self-study by practicing scientists and engineers and as a final-year undergraduate course or at the graduate level.

Computational Science Iccs 2002

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Author : Peter M.A. Sloot
language : en
Publisher: Springer
Release Date : 2003-08-01

Computational Science Iccs 2002 written by Peter M.A. Sloot and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-01 with Computers categories.

Computational Science is the scienti?c discipline that aims at the development and understanding of new computational methods and techniques to model and simulate complex systems. The area of application includes natural systems – such as biology, envir- mental and geo-sciences, physics, and chemistry – and synthetic systems such as electronics and ?nancial and economic systems. The discipline is a bridge b- ween ‘classical’ computer science – logic, complexity, architecture, algorithms – mathematics, and the use of computers in the aforementioned areas. The relevance for society stems from the numerous challenges that exist in the various science and engineering disciplines, which can be tackled by advances made in this ?eld. For instance new models and methods to study environmental issues like the quality of air, water, and soil, and weather and climate predictions through simulations, as well as the simulation-supported development of cars, airplanes, and medical and transport systems etc. Paraphrasing R. Kenway (R.D. Kenway, Contemporary Physics. 1994): ‘There is an important message to scientists, politicians, and industrialists: in the future science, the best industrial design and manufacture, the greatest medical progress, and the most accurate environmental monitoring and forecasting will be done by countries that most rapidly exploit the full potential ofcomputational science’. Nowadays we have access to high-end computer architectures and a large range of computing environments, mainly as a consequence of the enormous s- mulus from the various international programs on advanced computing, e.g.

Computational Science Iccs 2001

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Author : Vassil Alexandrov
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-05-24

Computational Science Iccs 2001 written by Vassil Alexandrov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-24 with Computers categories.

LNCS volumes 2073 and 2074 contain the proceedings of the International Conference on Computational Science, ICCS 2001, held in San Francisco, California, May 27 -31, 2001. The two volumes consist of more than 230 contributed and invited papers that reflect the aims of the conference to bring together researchers and scientists from mathematics and computer science as basic computing disciplines, researchers from various application areas who are pioneering advanced application of computational methods to sciences such as physics, chemistry, life sciences, and engineering, arts and humanitarian fields, along with software developers and vendors, to discuss problems and solutions in the area, to identify new issues, and to shape future directions for research, as well as to help industrial users apply various advanced computational techniques.

Computer Methods Part C

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Author :
language : en
Publisher: Academic Press
Release Date : 2010-12-24

Computer Methods Part C written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-24 with Science categories.

The combination of faster, more advanced computers and more quantitatively oriented biomedical researchers has recently yielded new and more precise methods for the analysis of biomedical data. These better analyses have enhanced the conclusions that can be drawn from biomedical data, and they have changed the way that experiments are designed and performed. This volume, along with the 2 previous Computer Methods volumes for the Methods in Enzymology serial, aims to inform biomedical researchers about recent applications of modern data analysis and simulation methods as applied to biomedical research. - Presents step-by-step computer methods and discusses the techniques in detail to enable their implementation in solving a wide range of problems - Informs biomedical researchers of the modern data analysis methods that have developed alongside computer hardware - Presents methods at the "nuts and bolts" level to identify and resolve a problem and analyze what the results mean

Practical Scientific Computing

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Author : Muhammad Ali
language : en
Publisher: Elsevier
Release Date : 2011-02-26

Practical Scientific Computing written by Muhammad Ali and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-26 with Mathematics categories.

Scientific computing is about developing mathematical models, numerical methods and computer implementations to study and solve real problems in science, engineering, business and even social sciences. Mathematical modelling requires deep understanding of classical numerical methods. This essential guide provides the reader with sufficient foundations in these areas to venture into more advanced texts.The first section of the book presents numEclipse, an open source tool for numerical computing based on the notion of MATLAB®. numEclipse is implemented as a plug-in for Eclipse, a leading integrated development environment for Java programming. The second section studies the classical methods of numerical analysis. Numerical algorithms and their implementations are presented using numEclipse.Practical scientific computing is an invaluable reference for undergraduate engineering, science and mathematics students taking numerical methods courses. It will also be a useful handbook for postgraduate researchers and professionals whose work involves scientific computing. - An invaluable reference for undergraduate engineering, science and mathematics students taking numerical methods courses - Guides the reader through developing a deep understanding of classical numerical methods - Features a comprehensive analysis of numEclipse including numerical algorithms and their implementations

Dynamic Systems Biology Modeling And Simulation

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Author : Joseph DiStefano III
language : en
Publisher: Academic Press
Release Date : 2015-01-10

Dynamic Systems Biology Modeling And Simulation written by Joseph DiStefano III and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-10 with Science categories.

Dynamic Systems Biology Modeling and Simuation consolidates and unifies classical and contemporary multiscale methodologies for mathematical modeling and computer simulation of dynamic biological systems – from molecular/cellular, organ-system, on up to population levels. The book pedagogy is developed as a well-annotated, systematic tutorial – with clearly spelled-out and unified nomenclature – derived from the author's own modeling efforts, publications and teaching over half a century. Ambiguities in some concepts and tools are clarified and others are rendered more accessible and practical. The latter include novel qualitative theory and methodologies for recognizing dynamical signatures in data using structural (multicompartmental and network) models and graph theory; and analyzing structural and measurement (data) models for quantification feasibility. The level is basic-to-intermediate, with much emphasis on biomodeling from real biodata, for use in real applications. - Introductory coverage of core mathematical concepts such as linear and nonlinear differential and difference equations, Laplace transforms, linear algebra, probability, statistics and stochastics topics - The pertinent biology, biochemistry, biophysics or pharmacology for modeling are provided, to support understanding the amalgam of "math modeling with life sciences - Strong emphasis on quantifying as well as building and analyzing biomodels: includes methodology and computational tools for parameter identifiability and sensitivity analysis; parameter estimation from real data; model distinguishability and simplification; and practical bioexperiment design and optimization - Companion website provides solutions and program code for examples and exercises using Matlab, Simulink, VisSim, SimBiology, SAAMII, AMIGO, Copasi and SBML-coded models - A full set of PowerPoint slides are available from the author for teaching from his textbook. He uses them to teach a 10 week quarter upper division course at UCLA, which meets twice a week, so there are 20 lectures. They can easily be augmented or stretched for a 15 week semester course - Importantly, the slides are editable, so they can be readily adapted to a lecturer's personal style and course content needs. The lectures are based on excerpts from 12 of the first 13 chapters of DSBMS. They are designed to highlight the key course material, as a study guide and structure for students following the full text content - The complete PowerPoint slide package (~25 MB) can be obtained by instructors (or prospective instructors) by emailing the author directly, at: [email protected]