Recent Developments In Numerical Methods And Software For Odes Daes Pdes

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Recent Developments in Numerical Methods and Software for ODEs/DAEs/PDEs

G D Byrne,W E Schiesser
Recent Developments in Numerical Methods and Software for ODEs DAEs PDEs Book PDF

Author : G D Byrne,W E Schiesser
Publisher : World Scientific
Page : 220 pages
File Size : 43,6 Mb
Release : 1992-03-27
Category : Mathematics
ISBN : 9789814506397

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Recent Developments in Numerical Methods and Software for ODEs/DAEs/PDEs by G D Byrne,W E Schiesser Pdf

Ordinary differential equations (ODEs), differential-algebraic equations (DAEs) and partial differential equations (PDEs) are among the forms of mathematics most widely used in science and engineering. Each of these equation types is a focal point for international collaboration and research. This book contains papers by recognized numerical analysts who have made important contributions to the solution of differential systems in the context of realistic applications, and who now report the latest results of their work in numerical methods and software for ODEs/DAEs/PDEs. The papers address parallelization and vectorization of numerical methods, the numerical solution of ODEs/DAEs/PDEs, and the use of these numerical methods in realistic scientific and engineering applications. Contents:An Overview of Recent Developments in Numerical Methods and Software for ODEs/DAEs/PDEs (G D Byrne & W E Schiesser)Experiments with an Ordinary Differential Equation Solver in the Parallel Solution of Method of Lines Problems on a Shared memory Parallel Computer (D K Kahaner et al.)Crayfishpak: A Vectorized Fortran Package to Solve Helmholtz Equations (R A Sweet)Experiments with an Adaptive H-, P-, R-Refinement Finite Element Method for Parabolic Systems (J E Flaherty & Y Wang)Incomplete Block Factorization Preconditioners: An Implementation for Block Tridiagonal Systems (D E Salane)Fast Generation of Weights in Finite Difference Formulas (B Fornberg)Numerical Methods for Boundary Value Problems in Differential-Algebraic Equations (U M Ascher & L R Petzold)The Solution of a Co-Polymerization Model with VODE (G D Byrne)Index Readership: Applied mathematicians, engineers and numerical analysts. keywords:Software;Numerical Methods;ODEs/DAEs/PDEs;Software;Numerical Methods;Ordinary Differential Equations;Differential-Algebraic Equations;Partial Differential Equations;Scientific and Engineering Applications

Recent Developments in Numerical Methods and Software for ODEs/DAEs/PDEs

George D. Byrne
Recent Developments in Numerical Methods and Software for ODEs DAEs PDEs Book PDF

Author : George D. Byrne
Publisher : World Scientific
Page : 226 pages
File Size : 51,8 Mb
Release : 1992
Category : Mathematics
ISBN : 9810205570

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Recent Developments in Numerical Methods and Software for ODEs/DAEs/PDEs by George D. Byrne Pdf

Ordinary differential equations (ODEs), differential-algebraic equations (DAEs) and partial differential equations (PDEs) are among the forms of mathematics most widely used in science and engineering. Each of these equation types is a focal point for international collaboration and research. This book contains papers by recognized numerical analysts who have made important contributions to the solution of differential systems in the context of realistic applications, and who now report the latest results of their work in numerical methods and software for ODEs/DAEs/PDEs. The papers address parallelization and vectorization of numerical methods, the numerical solution of ODEs/DAEs/PDEs, and the use of these numerical methods in realistic scientific and engineering applications.

Numerical Methods for Differential Systems

Leon Lapidus,W. E. Schiesser
Numerical Methods for Differential Systems Book PDF

Author : Leon Lapidus,W. E. Schiesser
Publisher : Unknown
Page : 312 pages
File Size : 44,8 Mb
Release : 1976
Category : Mathematics
ISBN : UOM:39015000979164

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Numerical Methods for Differential Systems by Leon Lapidus,W. E. Schiesser Pdf

Numerical Methods for Differential Systems.

Computational Mathematics in Engineering and Applied Science

W.E. Schiesser
Computational Mathematics in Engineering and Applied Science Book PDF

Author : W.E. Schiesser
Publisher : CRC Press
Page : 600 pages
File Size : 55,8 Mb
Release : 2014-07-22
Category : Mathematics
ISBN : 9781498710664

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Computational Mathematics in Engineering and Applied Science by W.E. Schiesser Pdf

Computational Mathematics in Engineering and Applied Science provides numerical algorithms and associated software for solving a spectrum of problems in ordinary differential equations (ODEs), differential algebraic equations (DAEs), and partial differential equations (PDEs) that occur in science and engineering. It presents detailed examples, each

Constrained Dynamics Computations

Bud Fox,Les S Jennings,Albert Y Zomaya
Constrained Dynamics Computations Book PDF

Author : Bud Fox,Les S Jennings,Albert Y Zomaya
Publisher : World Scientific
Page : 192 pages
File Size : 45,7 Mb
Release : 2000-09-04
Category : Technology & Engineering
ISBN : 9789814492720

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Constrained Dynamics Computations by Bud Fox,Les S Jennings,Albert Y Zomaya Pdf

This book introduces a practical approach to the modelling and computation of real-world systems. Multibody dynamics, planar and spatial modelling, and numerical methods are all pursued to obtain information about the behaviour of various dynamical systems. Each study presents the method of modelling and the ensuing differential equations governing the system behaviour. Integration of the equations yields results which are carefully discussed and which indicate how useful information may be obtained from the study. The studies include planar mechanisms, heavy equipment, automobile crash simulation and a spatial planetary system example. Research students, scientists and engineers will appreciate the practical approach taken in this book. Contents: OverviewPlanar ModellingNumerical MethodsPlanar Multibody SystemsOff-Highway Track VehicleAutomobile Crash SystemSpatial ModellingSpatial Planetary SystemConclusions and Future Directions Readership: Graduates, upper level undergraduates and researchers in mechanical engineering and mathematical modeling. Keywords:Dynamics;Modelling;Scientific Computation;Simulation;Multibody Systems;Differential Equations;Multi-Body Dynamics;Numerical Integration;Differential Algebraic Equations;DAE;Constrained Dynamics;Newton-Euler Equations;Automobile Crash Modelling

Constrained Dynamics Computations

Bud Fox,Leslie Stephen Jennings,Albert Y. Zomaya
Constrained Dynamics Computations Book PDF

Author : Bud Fox,Leslie Stephen Jennings,Albert Y. Zomaya
Publisher : World Scientific
Page : 200 pages
File Size : 44,5 Mb
Release : 2000
Category : Science
ISBN : 9812792538

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Constrained Dynamics Computations by Bud Fox,Leslie Stephen Jennings,Albert Y. Zomaya Pdf

A practical approach to the modelling and computation of real-world systems. Multibody dynamics, planar and spatial modelling, and numerical methods are all pursued to obtain information about the behaviour of various dynamical systems. Each study presents the method of modelling and the ensuing differential equations governing the system behaviour. Integration of the equations yields results which are carefully discussed and which indicate how useful information may be obtained from the study. The studies include planar mechanisms, heavy equipment, automobile crash simulation and a spatial planetary system example.

Recent Advances in Numerical Methods for Partial Differential Equations and Applications

Xiaobing Feng,Tim P. Schulze
Recent Advances in Numerical Methods for Partial Differential Equations and Applications Book PDF

Author : Xiaobing Feng,Tim P. Schulze
Publisher : American Mathematical Soc.
Page : 177 pages
File Size : 52,9 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821829707

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Recent Advances in Numerical Methods for Partial Differential Equations and Applications by Xiaobing Feng,Tim P. Schulze Pdf

An emerging field over the past 15 years, computational mathematics is a vast area which has experienced major developments in both algorithmic advances and applications to other fields. These developments have had profound implications in mathematics, science, engineering and industry. Compiled here are six of nine in-depth survey papers with an expository discussion on computational mathematics that were presented at the 2001 John H. Barrett Memorial Lectures at the University of Tennessee, Knoxville. They focus on parallel numerical algorithms for partial differential equations, their implementation and applications in fluid mechanics and material science. Each of the lecturers is a leading researcher in the field of computational mathematics and its applications. This book will be a useful reference for graduate students as well as the many groups of researchers working in advanced computations, including engineering and computer scientists. Prior knowledge of partial differential equations and their numerical methods is helpful.

Numerical Methods for PDEs

Daniele Antonio Di Pietro,Alexandre Ern,Luca Formaggia
Numerical Methods for PDEs Book PDF

Author : Daniele Antonio Di Pietro,Alexandre Ern,Luca Formaggia
Publisher : Springer
Page : 312 pages
File Size : 41,5 Mb
Release : 2018-10-12
Category : Mathematics
ISBN : 9783319946764

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Numerical Methods for PDEs by Daniele Antonio Di Pietro,Alexandre Ern,Luca Formaggia Pdf

This volume gathers contributions from participants of the Introductory School and the IHP thematic quarter on Numerical Methods for PDE, held in 2016 in Cargese (Corsica) and Paris, providing an opportunity to disseminate the latest results and envisage fresh challenges in traditional and new application fields. Numerical analysis applied to the approximate solution of PDEs is a key discipline in applied mathematics, and over the last few years, several new paradigms have appeared, leading to entire new families of discretization methods and solution algorithms. This book is intended for researchers in the field.

A Practical Guide to Pseudospectral Methods

Bengt Fornberg
A Practical Guide to Pseudospectral Methods Book PDF

Author : Bengt Fornberg
Publisher : Cambridge University Press
Page : 248 pages
File Size : 49,9 Mb
Release : 1998-10-28
Category : Mathematics
ISBN : 0521645646

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A Practical Guide to Pseudospectral Methods by Bengt Fornberg Pdf

This book explains how, when and why the pseudospectral approach works.

Numerical Integration of Space Fractional Partial Differential Equations

Younes Salehi,William E. Schiesser
Numerical Integration of Space Fractional Partial Differential Equations Book PDF

Author : Younes Salehi,William E. Schiesser
Publisher : Springer Nature
Page : 192 pages
File Size : 48,8 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 9783031024122

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Numerical Integration of Space Fractional Partial Differential Equations by Younes Salehi,William E. Schiesser Pdf

​ Partial differential equations (PDEs) are one of the most used widely forms of mathematics in science and engineering. PDEs can have partial derivatives with respect to (1) an initial value variable, typically time, and (2) boundary value variables, typically spatial variables. Therefore, two fractional PDEs can be considered, (1) fractional in time (TFPDEs), and (2) fractional in space (SFPDEs). The two volumes are directed to the development and use of SFPDEs, with the discussion divided as: Vol 1: Introduction to Algorithms and Computer Coding in R Vol 2: Applications from Classical Integer PDEs. Various definitions of space fractional derivatives have been proposed. We focus on the Caputo derivative, with occasional reference to the Riemann-Liouville derivative. In the second volume, the emphasis is on applications of SFPDEs developed mainly through the extension of classical integer PDEs to SFPDEs. The example applications are: Fractional diffusion equation with Dirichlet, Neumann and Robin boundary conditions Fisher-Kolmogorov SFPDE Burgers SFPDE Fokker-Planck SFPDE Burgers-Huxley SFPDE Fitzhugh-Nagumo SFPDE /div These SFPDEs were selected because they are integer first order in time and integer second order in space. The variation in the spatial derivative from order two (parabolic) to order one (first order hyperbolic) demonstrates the effect of the spatial fractional order with 1 ≤ ≤ 2. All of the example SFPDEs are one dimensional in Cartesian coordinates. Extensions to higher dimensions and other coordinate systems, in principle, follow from the examples in this second volume. The examples start with a statement of the integer PDEs that are then extended to SFPDEs. The format of each chapter is the same as in the first volume. The R routines can be downloaded and executed on a modest computer (R is readily available from the Internet).

Acta Numerica 1994: Volume 3

Arieh Iserles
Acta Numerica 1994 Volume 3 Book PDF

Author : Arieh Iserles
Publisher : Cambridge University Press
Page : 582 pages
File Size : 53,9 Mb
Release : 1994-07-29
Category : Mathematics
ISBN : 0521461812

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Acta Numerica 1994: Volume 3 by Arieh Iserles Pdf

Acta Numerica is an annual volume presenting survey papers in numerical analysis accessible to graduate students and researchers. Highlights of the 1994 issue are articles on domain decomposition, mesh adaption, pseudospectral methods and neural networks.

GPU Computing Gems Jade Edition

Wen-mei Hwu
GPU Computing Gems Jade Edition Book PDF

Author : Wen-mei Hwu
Publisher : Elsevier
Page : 562 pages
File Size : 48,7 Mb
Release : 2011-09-28
Category : Computers
ISBN : 9780123859631

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GPU Computing Gems Jade Edition by Wen-mei Hwu Pdf

"Since the introduction of CUDA in 2007, more than 100 million computers with CUDA capable GPUs have been shipped to end users. GPU computing application developers can now expect their application to have a mass market. With the introduction of OpenCL in 2010, researchers can now expect to develop GPU applications that can run on hardware from multiple vendors"--

Applications of Supercomputers in Engineering II

C.A. Brebbia,D. Howard,A. Peters
Applications of Supercomputers in Engineering II Book PDF

Author : C.A. Brebbia,D. Howard,A. Peters
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9789401136600

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Applications of Supercomputers in Engineering II by C.A. Brebbia,D. Howard,A. Peters Pdf

This book comprises an edited version of the Proceedings of the 2nd Interna tional Conference on Applications of Supercomputers in Engineering which took place at the Massachusetts Institute of Technology, Cambridge, USA during August 1991. The Conference was organized by the Wessex Insti tute of Technology, Southampton, UK with the support of the International Society for Boundary Elements. The first International Conference on Ap plications of Supercomputers in Engineering held in Southampton, UK in September 1989 was a very successful meeting and the resulting Conference Proceedings are now widely distributed throughout the world. The revolutionary aspects of the next generation of computers are now fully recognised by many engineers and scientists. Vector and parallel computers form the basis of the computing power needed to address the complex prob lems with which engineers are faced. The new machines not only increase the size of the problems which can be solved, but also require a different computational approach to obtain the most efficient results.

Modeling Biological Systems:

James W. Haefner
Modeling Biological Systems Book PDF

Author : James W. Haefner
Publisher : Springer Science & Business Media
Page : 500 pages
File Size : 42,8 Mb
Release : 2005-05-06
Category : Science
ISBN : 0387250115

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Modeling Biological Systems: by James W. Haefner Pdf

I Principles 1 1 Models of Systems 3 1. 1 Systems. Models. and Modeling . . . . . . . . . . . . . . . . . . . . 3 1. 2 Uses of Scientific Models . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 3 Example: Island Biogeography . . . . . . . . . . . . . . . . . . . . . 6 1. 4 Classifications of Models . . . . . . . . . . . . . . . . . . . . . . . . 10 1. 5 Constraints on Model Structure . . . . . . . . . . . . . . . . . . . . . 12 1. 6 Some Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1. 7 Misuses of Models: The Dark Side . . . . . . . . . . . . . . . . . . . 13 1. 8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 The Modeling Process 17 2. 1 Models Are Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2. 2 Two Alternative Approaches . . . . . . . . . . . . . . . . . . . . . . 18 2. 3 An Example: Population Doubling Time . . . . . . . . . . . . . . . . 24 2. 4 Model Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2. 5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3 Qualitative Model Formulation 32 3. 1 How to Eat an Elephant . . . . . . . . . . . . . . . . . . . . . . . . . 32 3. 2 Forrester Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3. 3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3. 4 Errors in Forrester Diagrams . . . . . . . . . . . . . . . . . . . . . . 44 3. 5 Advantages and Disadvantages of Forrester Diagrams . . . . . . . . . 44 3. 6 Principles of Qualitative Formulation . . . . . . . . . . . . . . . . . . 45 3. 7 Model Simplification . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3. 8 Other Modeling Problems . . . . . . . . . . . . . . . . . . . . . . . . 49 viii Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. 9 Exercises 53 4 Quantitative Model Formulation: I 4. 1 From Qualitative to Quantitative . . . . . . . . . . . . . . . . . Finite Difference Equations and Differential Equations 4. 2 . . . . . . . . . . . . . . . . 4. 3 Biological Feedback in Quantitative Models . . . . . . . . . . . . . . . . . . . . . . . . . . 4. 4 Example Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. 5 Exercises 5 Quantitative Model Formulation: I1 81 . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 1 Physical Processes 81 . . . . . . . . . . . . . . . 5. 2 Using the Toolbox of Biological Processes 89 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 3 Useful Functions 96 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 4 Examples 102 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 5 Exercises 104 6 Numerical Techniques 107 . . . . . . . . . . . . . . . . . . . . . . . 6. 1 Mistakes Computers Make 107 . . . . . . . . . . . . . . . . . . . . . . . . . . 6. 2 Numerical Integration 110 . . . . . . . . . . . . . . . . 6. 3 Numerical Instability and Stiff Equations 115 . . . . . . . . . . . . . .

Method of Lines PDE Analysis in Biomedical Science and Engineering

William E. Schiesser
Method of Lines PDE Analysis in Biomedical Science and Engineering Book PDF

Author : William E. Schiesser
Publisher : John Wiley & Sons
Page : 370 pages
File Size : 46,7 Mb
Release : 2016-04-13
Category : Mathematics
ISBN : 9781119130512

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Method of Lines PDE Analysis in Biomedical Science and Engineering by William E. Schiesser Pdf

Presents the methodology and applications of ODE and PDE models within biomedical science and engineering With an emphasis on the method of lines (MOL) for partial differential equation (PDE) numerical integration, Method of Lines PDE Analysis in Biomedical Science and Engineering demonstrates the use of numerical methods for the computer solution of PDEs as applied to biomedical science and engineering (BMSE). Written by a well-known researcher in the field, the book provides an introduction to basic numerical methods for initial/boundary value PDEs before moving on to specific BMSE applications of PDEs. Featuring a straightforward approach, the book’s chapters follow a consistent and comprehensive format. First, each chapter begins by presenting the model as an ordinary differential equation (ODE)/PDE system, including the initial and boundary conditions. Next, the programming of the model equations is introduced through a series of R routines that primarily implement MOL for PDEs. Subsequently, the resulting numerical and graphical solution is discussed and interpreted with respect to the model equations. Finally, each chapter concludes with a review of the numerical algorithm performance, general observations and results, and possible extensions of the model. Method of Lines PDE Analysis in Biomedical Science and Engineering also includes: Examples of MOL analysis of PDEs, including BMSE applications in wave front resolution in chromatography, VEGF angiogenesis, thermographic tumor location, blood-tissue transport, two fluid and membrane mass transfer, artificial liver support system, cross diffusion epidemiology, oncolytic virotherapy, tumor cell density in glioblastomas, and variable grids Discussions on the use of R software, which facilitates immediate solutions to differential equation problems without having to first learn the basic concepts of numerical analysis for PDEs and the programming of PDE algorithms A companion website that provides source code for the R routines Method of Lines PDE Analysis in Biomedical Science and Engineering is an introductory reference for researchers, scientists, clinicians, medical researchers, mathematicians, statisticians, chemical engineers, epidemiologists, and pharmacokineticists as well as anyone interested in clinical applications and the interpretation of experimental data with differential equation models. The book is also an ideal textbook for graduate-level courses in applied mathematics, BMSE, biology, biophysics, biochemistry, medicine, and engineering.