Approximate solution of differential equations with the use of asymptotic polynomials View Full Text


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Article Info

DATE

2012-02

AUTHORS

V. P. Gribkova, S. M. Kozlov

ABSTRACT

We consider an approximate solution of differential equations with initial and boundary conditions. To find a solution, we use asymptotic polynomials Qnf(x) of the first kind based on Chebyshev polynomials Tn(x) of the first kind and asymptotic polynomials Gnf(x) of the second kind based on Chebyshev polynomials Un(x) of the second kind. We suggest most efficient algorithms for each of these solutions. We find classes of functions for which the approximate solution converges to the exact one. The remainder is represented as an expansion in linear functionals {Lnf} in the first case and {Mnf} in the second case, whose decay rate depends on the properties of functions describing the differential equation. More... »

PAGES

264-274

Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/s0012266112020103

DOI

http://dx.doi.org/10.1134/s0012266112020103

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1015858903


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