Mathematics of Computation

An exponentially convergent algorithm for nonlinear differential equations in Banach spaces

Author(s): Ivan P. Gavrilyuk; Volodymyr L. Makarov.
Journal: Math. Comp. 76 (2007), 1895-1923.
MSC (2000): Primary 65J15, 65M15; Secondary 34G20, 35K90
Posted: April 19, 2007
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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.

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Retrieve articles in Mathematics of Computation with MSC (2000): 65J15, 65M15, 34G20, 35K90

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

DOI: 10.1090/S0025-5718-07-01987-4
PII: S 0025-5718(07)01987-4
Keywords: Nonlinear evolution equation, exponentially convergent algorithms, Sinc-methods
Received by editor(s): March 15, 2005
Received by editor(s) in revised form: June 30, 2006
Posted: April 19, 2007
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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