Illinois Journal of Mathematics

Expansion of solutions of parameterized equations and acceleration of numerical methods

István Gyöngy and Nicolai Krylov

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Abstract

A general scheme of parameterized families of equations is considered, and abstract results on the expansion of the solutions and on the acceleration of their convergence in terms of the parameter are presented. These results are applied to fractional step approximations for linear parabolic PDEs, systems of linear PDEs, and for nonlinear ordinary differential equations. Applications to accelerating the convergence of finite difference schemes for these equations will be presented in a subsequent paper.

Article information

Source
Illinois J. Math., Volume 50, Number 1-4 (2006), 473-514.

Dates
First available in Project Euclid: 12 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258059483

Digital Object Identifier
doi:10.1215/ijm/1258059483

Mathematical Reviews number (MathSciNet)
MR2247837

Zentralblatt MATH identifier
1123.65084

Subjects
Primary: 65B05: Extrapolation to the limit, deferred corrections
Secondary: 65L06: Multistep, Runge-Kutta and extrapolation methods 65M99: None of the above, but in this section

Citation

Gyöngy, István; Krylov, Nicolai. Expansion of solutions of parameterized equations and acceleration of numerical methods. Illinois J. Math. 50 (2006), no. 1-4, 473--514. doi:10.1215/ijm/1258059483. https://projecteuclid.org/euclid.ijm/1258059483


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