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＜電子ブック＞
Exponentially Convergent Algorithms for Abstract Differential Equations / by Ivan Gavrilyuk, Volodymyr Makarov, Vitalii Vasylyk
(Frontiers in Mathematics. ISSN:16608054)

版	1st ed. 2011.
出版者	(Basel : Springer Basel : Imprint: Birkhäuser)
出版年	2011
大きさ	VIII, 180 p. 12 illus : online resource
著者標目	*Gavrilyuk, Ivan author Makarov, Volodymyr author Vasylyk, Vitalii author SpringerLink (Online service)
件　名	LCSH:Mathematics FREE:Mathematics
一般注記	Preface -- 1 Introduction -- 2 Preliminaries -- 3 The first-order equations -- 4 The second-order equations -- Appendix: Tensor-product approximations of the operator exponential -- Bibliography -- Index This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as of partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which then can be applied to mathematical models of the real world. The problem class includes initial value problems (IVP) for first order differential equations with constant and variable unbounded operator coefficients in a Banach space (the heat equation is a simple example), boundary value problems for the second order elliptic differential equation with an operator coefficient (e.g. the Laplace equation), IVPs for the second order strongly damped differential equation as well as exponentially convergent methods to IVPs for the first order nonlinear differential equation with unbounded operator coefficients.  For researchers and students of numerical functional analysis, engineering and other sciences this book provides highly efficient algorithms for the numerical solution of differential equations and applied problems HTTP:URL=https://doi.org/10.1007/978-3-0348-0119-5

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