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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An exponentially convergent algorithm for nonlinear differential equations in Banach spaces
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by Ivan P. Gavrilyuk and Volodymyr L. Makarov;
Math. Comp. 76 (2007), 1895-1923
DOI: https://doi.org/10.1090/S0025-5718-07-01987-4
Published electronically: April 19, 2007

Abstract:

An exponentially convergent approximation to the solution of a nonlinear first order differential equation with an operator coefficient in Banach space is proposed. The algorithm is based on an equivalent Volterra integral equation including the operator exponential generated by the operator coefficient. The operator exponential is represented by a Dunford-Cauchy integral along a hyperbola enveloping the spectrum of the operator coefficient, and then the integrals involved are approximated using the Chebyshev interpolation and an appropriate Sinc quadrature. Numerical examples are given which confirm theoretical results.
References
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Bibliographic Information
  • Ivan P. Gavrilyuk
  • Affiliation: Staatliche Studienakademie Thueringen-Berufsakademie Eisenach, University of Cooperative Edukation, Am Wartenberg 2, D-99817 Eisenach, Germany
  • Email: ipg@ba-eisenach.de
  • Volodymyr L. Makarov
  • Affiliation: National Academy of Sciences of Ukraine, Institute of Mathematics, Tereschenkivska 3, 01601 Kiev, Ukraine
  • Email: makarov@imath.kiev.ua
  • Received by editor(s): March 15, 2005
  • Received by editor(s) in revised form: June 30, 2006
  • Published electronically: April 19, 2007
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 76 (2007), 1895-1923
  • MSC (2000): Primary 65J15, 65M15; Secondary 34G20, 35K90
  • DOI: https://doi.org/10.1090/S0025-5718-07-01987-4
  • MathSciNet review: 2336273