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Exponentially Convergent Algorithms for Abstract Differential Equations

  • Ivan Gavrilyuk
  • Volodymyr Makarov
  • Vitalii Vasylyk

Part of the Frontiers in Mathematics book series (FM)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Ivan Gavrilyuk, Volodymyr Makarov, Vitalii Vasylyk
    Pages 1-8
  3. Ivan Gavrilyuk, Volodymyr Makarov, Vitalii Vasylyk
    Pages 9-22
  4. Ivan Gavrilyuk, Volodymyr Makarov, Vitalii Vasylyk
    Pages 23-125
  5. Ivan Gavrilyuk, Volodymyr Makarov, Vitalii Vasylyk
    Pages 127-165
  6. Back Matter
    Pages 167-180

About this book

Introduction

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.

Authors and affiliations

  • Ivan Gavrilyuk
    • 1
  • Volodymyr Makarov
    • 2
  • Vitalii Vasylyk
    • 3
  1. 1.Berufsakademie Eisenach, UniversityStaatliche Studienakademie ThüringenEisenachGermany
  2. 2., Institute of MathematicsNational Academy of Sciences of UkraineKiev-4Ukraine
  3. 3., Institute of MathematicsNational Academy of Sciences of UkraineKiev-4Ukraine

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0119-5
  • Copyright Information Springer Basel AG 2011
  • Publisher Name Springer, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0118-8
  • Online ISBN 978-3-0348-0119-5
  • Series Print ISSN 1660-8046
  • Series Online ISSN 1660-8054
  • Buy this book on publisher's site