Solution of a singular integro-differential equation with the use of asymptotic polynomials

Autor:	V. P. Gribkova, S. M. Kozlov
Rok vydání:	2013
Předmět:	Polynomial Chebyshev polynomials Difference polynomials Singular solution General Mathematics Ordinary differential equation ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Mathematical analysis Polynomial remainder theorem Degree of a polynomial Remainder Analysis Mathematics
Zdroj:	Differential Equations. 49:1150-1159
ISSN:	1608-3083 0012-2661
DOI:	10.1134/s0012266113090103
Popis:	We suggest a new method for solving a singular equation of elasticity theory, which is based on the use of asymptotic polynomials constructed on the basis of Chebyshev polynomials of the second kind. Under certain conditions imposed on the functions occurring in the operator equation, the approximate solution tends as n → ∞ to the best uniform approximation polynomial, which converges to the exact solution as n increases. The method permits one to express the remainder term of the approximate solution in the form of an infinite sum via linear functionals. If the originally chosen degree of the polynomial does not provide the desired accuracy, then one can find the corresponding term of the remainder starting from which the desired accuracy is attained and compute the polynomial of the corresponding degree. The proof of the convergence is presented for the case in which the variable ranges in a closed interval.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::1cea9d08f1911bf29da9ce7a5cc5d836 https://doi.org/10.1134/s0012266113090103 Zobrazit plný text záznamu Plný text ve formátu PDF