Numerical Analysis Using R Solutions to ODEs and PDEs

This book presents the latest numerical solutions to initial value problems and boundary value problems described by ODEs and PDEs. The author offers practical methods that can be adapted to solve wide ranges of problems and illustrates them in the increasingly popular open source computer language...

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Hlavní autor: Griffiths, Graham W.
Médium: E-kniha Kniha
Jazyk:angličtina
Vydáno: New York, N.Y Cambridge University Press 26.04.2016
Témata:
Boundary value problems
Boundary value problems > Data processing
Differential equations
Differential equations > Data processing
Differential equations, Partial
Differential equations, Partial > Data processing
General Engineering & Project Administration
General References
Initial value problems
Initial value problems > Data processing
Numerical analysis
R (Computer program language)
ISBN:9781107115613, 1107115612
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Abstract This book presents the latest numerical solutions to initial value problems and boundary value problems described by ODEs and PDEs. The author offers practical methods that can be adapted to solve wide ranges of problems and illustrates them in the increasingly popular open source computer language R, allowing integration with more statistically based methods. The book begins with standard techniques, followed by an overview of 'high resolution' flux limiters and WENO to solve problems with solutions exhibiting high gradient phenomena. Meshless methods using radial basis functions are then discussed in the context of scattered data interpolation and the solution of PDEs on irregular grids. Three detailed case studies demonstrate how numerical methods can be used to tackle very different complex problems. With its focus on practical solutions to real-world problems, this book will be useful to students and practitioners in all areas of science and engineering, especially those using R.
AbstractList This book presents the latest numerical solutions to initial value problems and boundary value problems described by ODEs and PDEs. The author offers practical methods that can be adapted to solve wide ranges of problems and illustrates them in the increasingly popular open source computer language R, allowing integration with more statistically based methods. The book begins with standard techniques, followed by an overview of 'high resolution' flux limiters and WENO to solve problems with solutions exhibiting high gradient phenomena. Meshless methods using radial basis functions are then discussed in the context of scattered data interpolation and the solution of PDEs on irregular grids. Three detailed case studies demonstrate how numerical methods can be used to tackle very different complex problems. With its focus on practical solutions to real-world problems, this book will be useful to students and practitioners in all areas of science and engineering, especially those using R.
Author Griffiths, Graham W.
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2016
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Notes Includes bibliographical references (p. 581-583) and index
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SubjectTerms Boundary value problems
Boundary value problems -- Data processing
Differential equations
Differential equations -- Data processing
Differential equations, Partial
Differential equations, Partial -- Data processing
General Engineering & Project Administration
General References
Initial value problems
Initial value problems -- Data processing
Numerical analysis
R (Computer program language)
Subtitle Solutions to ODEs and PDEs
TableOfContents Title Page About This Book Preface Table of Contents 1. ODE Integration Methods 2. Stability Analysis of ODE Integrators 3. Numerical Solution of PDEs 4. PDE Stability Analysis 5. Dissipation and Dispersion 6. High-Resolution Schemes 7. Meshless Methods 8. Conservation Laws 9. Case Study: Analysis of Golf Ball Flight 10. Case Study: Taylor-Sedov Blast Wave 11. Case Study: The Carbon Cycle Appendix: A Mathematical Aide-Mémoire Index Color Plates
Title Numerical Analysis Using R
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