General Linear Methods For Ordinary Differential Equations,New

General Linear Methods For Ordinary Differential Equations,New

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Learn to develop numerical methods for ordinary differential equationsGeneral Linear Methods for Ordinary Differential Equations fills a gap in the existing literature by presenting a comprehensive and uptodate collection of recent advances and developments in the field. This book provides modern coverage of the theory, construction, and implementation of both classical and modern general linear methods for solving ordinary differential equations as they apply to a variety of related areas, including mathematics, applied science, and engineering.The author provides the theoretical foundation for understanding basic concepts and presents a short introduction to ordinary differential equations that encompasses the related concepts of existence and uniqueness theory, stability theory, and stiff differential equations and systems. In addition, a thorough presentation of general linear methods explores relevant subtopics such as preconsistency, consistency, stageconsistency, zero stability, convergence, order and stageorder conditions, local discretization error, and linear stability theory. Subsequent chapters feature coverage of: Differential equations and systemsIntroduction to general linear methods (GLMs)Diagonally implicit multistage integration methods (DIMSIMs)Implementation of DIMSIMsTwostep RungeKutta (TSRK) methodsImplementation of TSRK methodsGLMs with inherent RungeKutta stability (IRKS)Implementation of GLMs with IRKSGeneral Linear Methods for Ordinary Differential Equations is an excellent book for courses on numerical ordinary differential equations at the upperundergraduate and graduate levels. It is also a useful reference for academic and research professionals in the fields of computational and applied mathematics, computational physics, civil and chemical engineering, chemistry, and the life sciences.

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