Numerical Methods for Differential Systems
Recent Developments in Algorithms, Software, and Applications
- 304 pages
- English
- PDF
- Available on iOS & Android
Numerical Methods for Differential Systems
Recent Developments in Algorithms, Software, and Applications
About this book
Numerical Methods for Differential Systems: Recent Developments in Algorithms, Software, and Applications reviews developments in algorithms, software, and applications of numerical methods for differential systems. Topics covered include numerical algorithms for ordinary and partial differential equations (ODE/PDEs); theoretical approaches to the solution of nonlinear algebraic and boundary value problems via associated differential systems; integration algorithms for initial-value ODEs with particular emphasis on stiff systems; finite difference algorithms; and general- and special-purpose computer codes for ODE/PDEs. Comprised of 15 chapters, this book begins with an introduction to high-order A-stable averaging algorithms for stiff differential systems, followed by a discussion on second derivative multistep formulas based on g-splines; numerical integration of linearized stiff ODEs; and numerical solution of large systems of stiff ODEs in a modular simulation framework. Subsequent chapters focus on numerical methods for mass action kinetics; a systematized collection of codes for solving two-point boundary value problems; general software for PDEs; and the choice of algorithms in automated method of lines solution of PDEs. The final chapter is devoted to quality software for ODEs. This monograph should be of interest to mathematicians, chemists, and chemical engineers.
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Table of contents
- Front Cover
- Numerical Methods for Differential Systems: Recent Developments in Algorithms, Software, and Applications
- Copyright Page
- Table of Contents
- List of Contributors
- Preface
- Chapter 1. High-Order A-Stable Averaging Algorithms for Stiff Differential Systems
- Chapter 2. Second Derivative Multistep Formulas Based on g-Splines
- Chapter 3. Numerical Integration of Linearized Stiff Ordinary Differential Equations
- Chapter 4. Comparing Numerical Methods for the Solution of Stiff Systems of ODEs Arising in Chemistry
- Chapter 5. On the Construction of Differential Systems for the Solution of Nonlinear Algebraic and Transcendental Systems of Equations
- Chapter 6. Differential Procedures for Systems of Implicit Relations and Implicitly Coupled Nonlinear Boundary-Value Problems
- Chapter 7. Numerical Solution of Large Systems of Stiff Ordinary Differential Equations in a Modular Simulation Framework
- Chapter 8. FAST: A Translator for the Solution of Stiff and Nonlinear Differential and Algebraic Equations
- Chapter 9. Applications of EPISODE: An Experimental Package for the Integration of Systems of Ordinary Differential Equations
- Chapter 10. SETKIN: A Chemical Kenetics Preprocessor Code
- Chapter 11. Numerical Methods for Mass Action Kinetics
- Chapter 12. A Systematized Collection of Codes for Solving Two-Point Boundary-Value Problems
- Chapter 13. General Software for Partial Differential Equations
- Chapter 14. The Choice of Algorithms in Automated Methodof Lines Solution of Partial Differential Equations
- Chapter 15. Panel Discussion of Quality Software for ODEs
- Subject Index