Linear Discrete Parabolic Problems

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Author: Nikolai Bakaev

Publisher: Elsevier

ISBN: 9780080462080

Category: Mathematics

Page: 302

View: 3965

This volume introduces a unified, self-contained study of linear discrete parabolic problems through reducing the starting discrete problem to the Cauchy problem for an evolution equation in discrete time. Accessible to beginning graduate students, the book contains a general stability theory of discrete evolution equations in Banach space and gives applications of this theory to the analysis of various classes of modern discretization methods, among others, Runge-Kutta and linear multistep methods as well as operator splitting methods. Key features: * Presents a unified approach to examining discretization methods for parabolic equations. * Highlights a stability theory of discrete evolution equations (discrete semigroups) in Banach space. * Deals with both autonomous and non-autonomous equations as well as with equations with memory. * Offers a series of numerous well-posedness and convergence results for various discretization methods as applied to abstract parabolic equations; among others, Runge-Kutta and linear multistep methods as well as certain operator splitting methods. * Provides comments of results and historical remarks after each chapter. · Presents a unified approach to examining discretization methods for parabolic equations. · Highlights a stability theory of discrete evolution equations (discrete semigroups) in Banach space. · Deals with both autonomous and non-autonomous equations as well as with equations with memory. · Offers a series of numerous well-posedness and convergence results for various discretization methods as applied to abstract parabolic equations; among others, Runge-Kutta and linear multistep methods as well as certain operator splitting methods as well as certain operator splitting methods are studied in detail. ·Provides comments of results and historical remarks after each chapter.

Galerkin Finite Element Methods for Parabolic Problems

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Author: Vidar Thomee

Publisher: Springer Science & Business Media

ISBN: 3540331220

Category: Mathematics

Page: 364

View: 517

This book provides insight into the mathematics of Galerkin finite element method as applied to parabolic equations. The revised second edition has been influenced by recent progress in application of semigroup theory to stability and error analysis, particulatly in maximum-norm. Two new chapters have also been added, dealing with problems in polygonal, particularly noncovex, spatial domains, and with time discretization based on using Laplace transformation and quadrature.

Advanced Numerical Methods for Complex Environmental Models: Needs and Availability

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Author: István Faragó,Ágnes Havasi,Zahari Zlatev

Publisher: Bentham Science Publishers

ISBN: 160805778X

Category: Nature

Page: 426

View: 9110

High air pollution levels pose a significant threat to plants, animals and human beings. Efforts by researchers are directed towards keeping air pollution levels below well defined ‘critical‘ levels in order to maintain a sustainable atmosphere and environmental system. The application of advanced mathematical models is important for researchers to achieve this goal as efficiently as possible. Mathematical models can be used to predict answers to many important questions about the environment. This application comes with several complex theoretical and practical obstacles which need to be resolved. A successfully applicable mathematical model needs to enable researchers to • Mathematically describe all important physical and chemical processes. • Apply fast and sufficiently accurate numerical methods. • Ensure that the model runs efficiently on modern high speed computers. • Use high quality input data, both meteorological data and emission inventories, in the runs. • Verify the model results by comparing them with reliable measurements taken in different parts of the spatial domain of the model. • Carry out long series of sensitivity experiments to check the response of the model to changes of different key parameters. • Visualize and animate the output results in order to make them easily understandable even to non-specialists. This monograph thoroughly describes mathematical methods useful for various situations in environmental modeling - including finite difference methods, splitting methods, parallel computation, etc. - and provides a framework for resolving problems posed in relation to the points listed above. Chapters are written by well-known specialists making this book a handy reference for researchers, university teachers and students working and studying in the areas of air pollution, meteorology, applied mathematics and computer science.

DCDS-A

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

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