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Bakaev N.Y. — Linear Discrete Parabolic Problems

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Название: Linear Discrete Parabolic Problems

Автор: Bakaev N.Y.

Аннотация:

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.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 302

Добавлена в каталог: 22.05.2008

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Предметный указатель

Amplification matrix      231
Backward Euler method      100 248
BDF method      241
Commutator      54
contour      258
Convexity inequality      261
Crank — Nicolson method      100 251
Discrete evolution operator      4
Discrete semigroup      4 19
Equation with memory      71
Equation, integro-differential      245
Evolution equation in discrete time      4 19
Family of grids, exponentially balanced      185
Family of grids, locally balanced      186
Family, quasi-quasiuniform grids      186
Family, quasi-uniform grids      187
Fractional power      260
Function of linear operator      258
Function of ordered operators      262
Functional $Q_n(\dot)$       148
Functional $Q_{nj}(\dot)$       148
Gauss — Legendre method      99
Hypothesis, $hol^*_{(k)}[...]$       232
Hypothesis, $HOL^{(\leftarrow)}(...)$       33
Hypothesis, $hOl^{(\rightarrow)}(...)$       33
Hypothesis, $hol^{\oplus}[...]$       84
Hypothesis, $hol^{\oplus}_{(k)}[...]$       85
Hypothesis, COM1[...]      54
Hypothesis, COM2[...]      54
Hypothesis, HOL(...)      33
Hypothesis, hol[...]      84
Hypothesis, lip      86
Hypothesis, llp(...)      86
Integration path      258
Linear multistep method      228
Linear multistep method of class       231
Linear multistep method of type $LM(\varphi)$       231
Linear multistep method of type $LM_I(\varphi)$       232
Lobatto method      100
Methods with splitting operator      219
Non-uniform grid (partition)      179
Operator splitting      53
Operator, $(M; \varphi, \sigma)$ -sectorial      124
Operator, $(\varphi, \sigma)$ -sectorial      xiii
Order of approach      155
Order of single step method      98

Order reduction      157 173
Order, polynomial      98
Order, stage      98
Ordered sequence      185
Pair, $\Lambda_J(...)$ -concordant      7
Pair, $\Lambda_J^k(...)$ -concordant      6 19
Pair, (...)-concordant      86
Pair, strictly $\Lambda_J(...)$ -concordant      7
Pair, strictly $\Lambda_J^k(...)$ -concordant      7
Pair, strictly (...)-concordant      86
Parabolic case      xiii
Parabolic differential equations      xiii
Parameters of set of $\Lambda_J$ -configuration      5
Radau method      100
RK method      95
RK method, $A(\varphi)$ -stable      96
RK method, -stable      97
RK method, $A_J(\varphi)$ -stable      97
RK method, A-stable      96
RK method, of class       97
RK method, of type $C(\varphi)$       96
RK method, of type $C_J(\varphi)$       97
RK method, of type $V(\varphi)$       96
RK method, of type $V*(\varphi)$       96
RK method, of type $V_J(\varphi)$       97
RK method, of type $V_J*(\varphi)$       97
Sectorial estimate      xiii
Set of $\Lambda_J$ -configuration      5
Set, $\Lambda_J$ -proper      6 25
Set, $\Lambda_J(...)$ -proper      7
Set, $\Lambda_J^k$ -proper      6
Set, $\Lambda_J^k(...)$ -proper      7
Simplifying assumptions      98
Singular points of operator      6
Singular points of set of $\Lambda_J$ -configuration      5
Solution of Cauchy problem      265
Solution of multistep procedure, C-extended      229
Solution of multistep procedure, V-extended      229
Solution, classical      265
Solution, extended, of Cauchy problem      266
Solution, extended, of order p      266
Solution, extended, of Runge — Kutta procedure      104 148 180
Sparse quadrature rule      252
Stability function      95
Testing functional      85 232
Triplet, $\Lambda_J(...)$ -concordant      7
Triplet, $\Lambda_J^k(...)$ -concordant      7

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