| Edition |
1st ed. |
| Description |
1 online resource (xv, 286 pages) |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
North-Holland mathematics studies, 0304-0208 ; 203 |
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North-Holland mathematics studies ; 203. 0304-0208
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| Summary |
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. |
| Contents |
Preface. -- Part I. EVOLUTION EQUATIONS IN DISCRETE TIME. -- Preliminaries. -- Main Results on Stability. -- Operator Splitting Problems. -- Equations with Memory. -- Part II. RUNGE-KUTTA METHODS. -- Discretization by Runge-Kutta methods. -- Analysis of Stability. -- Convergence Estimates. -- Variable Stepsize Approximations. -- Part III. OTHER DISCRETIZATION METHODS. -- The/theta-method. -- Methods with Splitting Operator. -- Linear Multistep Methods. -- Part IV. INTEGRO-DIFFERENTIAL EQUATIONS UNDER DISCRETIZATION. -- Integro-Differential Equations. -- APPENDIX. -- A Functions of Linear Operators. -- B Cauchy Problems in Banach Space. |
| Bibliography |
Includes bibliographical references (pages 269-283) and index. |
| Note |
Print version record. |
| Subject |
Stability.
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Runge-Kutta formulas.
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Differential equations.
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Computer science -- Mathematics.
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Stabilité.
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Méthode de Runge-Kutta.
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Équations différentielles.
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Informatique -- Mathématiques.
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stability.
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MATHEMATICS -- Differential Equations -- General.
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Computer science -- Mathematics
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Differential equations
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Runge-Kutta formulas
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Stability
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| Other Form: |
Print version: Bakaev, Nikolai Yu. Linear discrete parabolic problems. 1st ed. Amsterdam ; Boston : Elsevier, 2006 0444521402 9780444521408 (DLC) 2005055340 (OCoLC)62408816 |
| ISBN |
9780444521408 |
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0444521402 |
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0080462081 (electronic bk.) |
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9780080462080 (electronic bk.) |
| Standard No. |
AU@ 000048130514 |
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AU@ 000051860873 |
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CHNEW 001006658 |
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DEBBG BV036962359 |
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DEBBG BV039830227 |
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DEBBG BV042317351 |
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DEBSZ 276322169 |
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DEBSZ 482355964 |
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NZ1 12435170 |
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AU@ 000075306984 |
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