00000cmm a22000004a 4500 UP-99796217611212299 Buklod 20230215085534.0 m go u cr |n |||auu|a 110715s2011 xx u eng d 9783034801195 (eBook) 303480119X (eBook) (iLib)UPD-00215704058 DML eng DMLUC QA 371 G38 2011eb Gavrilyuk, Ivan P. Exponentially convergent algorithms for abstract differential equations [electronic resource] Ivan Gavrilyuk, Volodymyr Makarov, Vitalii Vasylyk. Basel [New York] Birkhèauser Springer c2011. 1 online resource (viii, 180 p.) ill. Frontiers in mathematics 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. IP-based subscription, access limited to within on-campus computer network. Access via Electronic Resources of the UPD University Library Website. "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 the 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 the 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"--P. [4] of cover. Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through SpringerLink. Differential equations. Electronic books. Makarov, Volodymyr. Vasylyk, Vitalii. SpringerLink (Online service). Electronic Resource Available for University of the Philippines Diliman via SpringerLink. Click here to access http://dx.doi.org/10.1007/978-3-0348-0119-5 FO Monograph UPD DMLR Electronic Resource