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.
List of Contributors
High-Order A-Stable Averaging Algorithms for Stiff Differential Systems
Second Derivative Multistep Formulas Based on g-Splines
Numerical Integration of Linearized Stiff Ordinary Differential Equations
Comparing Numerical Methods for the Solution of Stiff Systems of ODEs Arising in Chemistry
On the Construction of Differential Systems for the Solution of Nonlinear Algebraic and Transcendental Systems of Equations
Differential Procedures for Systems of Implicit Relations and Implicitly Coupled Nonlinear Boundary Value Problems
Numerical Solution of Large Systems of Stiff Ordinary Differential Equations in a Modular Simulation Framework
FAST: A Translator for the Solution of Stiff and Nonlinear Differential and Algebraic Equations
Applications of EPISODE: An Experimental Package for the Integration of Systems of Ordinary Differential Equations
SETKIN: A Chemical Kinetics Preprocessor Code
Numerical Methods for Mass Action Kinetics
A Systematized Collection of Codes for Solving Two-Point Boundary-Value Problems
General Software for Partial Differential Equations
The Choice of Algorithms in Automated Method of Lines Solution of Partial Differential Equations
Panel Discussion of Quality Software for ODEs
- No. of pages:
- © Academic Press 1976
- 1st January 1976
- Academic Press
- eBook ISBN:
DEPARTMENT OF CHEMICAL ENGINEERING PRINCETON UNIVERSITY PRINCETON, NEW JERSEY
W.E. Schiesser is Emeritus McCann Professor of Chemical and Biomolecular Engineering and Professor of Mathematics at Lehigh University. He holds a PhD from Princeton University and a ScD (hon) from the University of Mons, Belgium. His research is directed toward numerical methods and associated software for ordinary, differential-algebraic and partial differential equations (ODE/DAE/PDEs), and the development of mathematical models based on ODE/DAE/PDEs. He is the author or coauthor of more than 14 books, and his ODE/DAE/PDE computer routines have been accessed by some 5,000 colleges and universities, corporations and government agencies.
Emeritus R.L. McCann Professor of Chemical and Biomolecular Engineering, Professor of Mathematics, Lehigh University, Bethlehem, PA, USA