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![]( "Buchcover ISBN 9780470522158")
General Linear Methods for Ordinary Differential Equations
von Zdzislaw JackiewiczLearn to develop numerical methods for ordinary differentialequations
General Linear Methods for Ordinary Differential Equations fillsa gap in the existing literature by presenting a comprehensive andup-to-date collection of recent advances and developments in thefield. This book provides modern coverage of the theory, construction, and implementation of both classical and moderngeneral linear methods for solving ordinary differential equationsas they apply to a variety of related areas, including mathematics, applied science, and engineering.
The author provides the theoretical foundation for understandingbasic concepts and presents a short introduction to ordinarydifferential equations that encompasses the related concepts ofexistence and uniqueness theory, stability theory, and stiffdifferential equations and systems. In addition, a thoroughpresentation of general linear methods explores relevant subtopicssuch as pre-consistency, consistency, stage-consistency, zerostability, convergence, order- and stage-order conditions, localdiscretization error, and linear stability theory. Subsequentchapters feature coverage of:
* Differential equations and systems
* Introduction to general linear methods (GLMs)
* Diagonally implicit multistage integration methods (DIMSIMs)
* Implementation of DIMSIMs
* Two-step Runge-Kutta (TSRK) methods
* Implementation of TSRK methods
* GLMs with inherent Runge-Kutta stability (IRKS)
* Implementation of GLMs with IRKS
General Linear Methods for Ordinary Differential Equations is anexcellent book for courses on numerical ordinary differentialequations at the upper-undergraduate and graduate levels. It isalso a useful reference for academic and research professionals inthe fields of computational and applied mathematics, computationalphysics, civil and chemical engineering, chemistry, and the lifesciences.
General Linear Methods for Ordinary Differential Equations fillsa gap in the existing literature by presenting a comprehensive andup-to-date collection of recent advances and developments in thefield. This book provides modern coverage of the theory, construction, and implementation of both classical and moderngeneral linear methods for solving ordinary differential equationsas they apply to a variety of related areas, including mathematics, applied science, and engineering.
The author provides the theoretical foundation for understandingbasic concepts and presents a short introduction to ordinarydifferential equations that encompasses the related concepts ofexistence and uniqueness theory, stability theory, and stiffdifferential equations and systems. In addition, a thoroughpresentation of general linear methods explores relevant subtopicssuch as pre-consistency, consistency, stage-consistency, zerostability, convergence, order- and stage-order conditions, localdiscretization error, and linear stability theory. Subsequentchapters feature coverage of:
* Differential equations and systems
* Introduction to general linear methods (GLMs)
* Diagonally implicit multistage integration methods (DIMSIMs)
* Implementation of DIMSIMs
* Two-step Runge-Kutta (TSRK) methods
* Implementation of TSRK methods
* GLMs with inherent Runge-Kutta stability (IRKS)
* Implementation of GLMs with IRKS
General Linear Methods for Ordinary Differential Equations is anexcellent book for courses on numerical ordinary differentialequations at the upper-undergraduate and graduate levels. It isalso a useful reference for academic and research professionals inthe fields of computational and applied mathematics, computationalphysics, civil and chemical engineering, chemistry, and the lifesciences.
