Exponentially convergent algorithms for abstract differential equations [Documento electrónico] / Ivan Gavrilyuk, Volodymyr Makarov, Vitalii Vasylyk
Language: eng.Country: Switzerland, Swiss Confederation.Publication: Basel : Springer , 2011Description: VIII, 180p. : il.ISBN: 978-3-0348-0119-5.Series: Frontiers in MathematicsSubject - Topical Name: Equações diferenciais Online Resources:Click here to access onlineItem type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
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QA371.SPR FCT 81480 Differential equations, a primer for scientists and engineers | QA371.SPR FCT 81536 Lyapunov-type inequalities, with applications to eigenvalue problems | QA371.SPR FCT 81591 Ergodic theory, open dynamics, and coherent structures | QA371.SPR FCT 81738 Exponentially convergent algorithms for abstract differential equations | QA371.SPR FCT 81773 Stability of vector differential delay equations | QA371.SPR FCT 81792 Introduction to the qualitative theory of differential systems, planar, symmetric and continuous piecewise linear systems | QA371.SPR FCT 81825 Green's Kernels and meso-scale approximations in perforated domains |
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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.
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