Galerkin/Runge-Kutta Discretizations for Semilinear Parabolic Equations PDF Download
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Author: Stephen L. Keeling
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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Author: Stephen L. Keeling
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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Book Description
Author: Stephen Louis Keeling
Publisher:
ISBN:
Category : Galerkin methods
Languages : en
Pages : 36
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Book Description
Author: Stephen L. Keeling
Publisher:
ISBN:
Category :
Languages : en
Pages : 46
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Book Description
Author: Stephen Louis Keeling
Publisher:
ISBN:
Category : Differential equations, Parabolic
Languages : en
Pages : 652
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Author: Vidar Thomée
Publisher: Springer Science & Business Media
ISBN: 9783540632368
Category :
Languages : en
Pages : 320
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Author: Vidar Thomee
Publisher: Springer Science & Business Media
ISBN: 3662033593
Category : Mathematics
Languages : en
Pages : 310
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Book Description
My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin finite element methods as applied to parabolic partial differential equations. The emphases and selection of topics reflects my own involvement in the field over the past 25 years, and my ambition has been to stress ideas and methods of analysis rather than to describe the most general and farreaching results possible. Since the formulation and analysis of Galerkin finite element methods for parabolic problems are generally based on ideas and results from the corresponding theory for stationary elliptic problems, such material is often included in the presentation. The basis of this work is my earlier text entitled Galerkin Finite Element Methods for Parabolic Problems, Springer Lecture Notes in Mathematics, No. 1054, from 1984. This has been out of print for several years, and I have felt a need and been encouraged by colleagues and friends to publish an updated version. In doing so I have included most of the contents of the 14 chapters of the earlier work in an updated and revised form, and added four new chapters, on semigroup methods, on multistep schemes, on incomplete iterative solution of the linear algebraic systems at the time levels, and on semilinear equations. The old chapters on fully discrete methods have been reworked by first treating the time discretization of an abstract differential equation in a Hilbert space setting, and the chapter on the discontinuous Galerkin method has been completely rewritten.
Author: Nikolai Bakaev
Publisher: Elsevier
ISBN: 0080462081
Category : Mathematics
Languages : en
Pages : 303
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Book Description
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.
Author: Atsushi Yagi
Publisher: Springer Science & Business Media
ISBN: 3642046312
Category : Mathematics
Languages : en
Pages : 594
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Book Description
This monograph is intended to present the fundamentals of the theory of abstract parabolic evolution equations and to show how to apply to various nonlinear dif- sion equations and systems arising in science. The theory gives us a uni?ed and s- tematic treatment for concrete nonlinear diffusion models. Three main approaches are known to the abstract parabolic evolution equations, namely, the semigroup methods, the variational methods, and the methods of using operational equations. In order to keep the volume of the monograph in reasonable length, we will focus on the semigroup methods. For other two approaches, see the related references in Bibliography. The semigroup methods, which go back to the invention of the analytic se- groups in the middle of the last century, are characterized by precise formulas representing the solutions of the Cauchy problem for evolution equations. The ?tA analytic semigroup e generated by a linear operator ?A provides directly a fundamental solution to the Cauchy problem for an autonomous linear e- dU lution equation, +AU =F(t), 0
Author: K. Antreich
Publisher: Birkhäuser
ISBN: 3034880650
Category : Mathematics
Languages : en
Pages : 356
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Book Description
The third Conference on Mathematical Models and Numerical Simulation in Electronic Industry brought together researchers in mathematics, electrical engineering and scientists working in industry. The contributions to this volume try to bridge the gap between basic and applied mathematics, research in electrical engineering and the needs of industry.
Author: Daniel Henry
Publisher: Springer
ISBN: 3540385282
Category : Mathematics
Languages : en
Pages : 353
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Book Description
