Nyström methods for approximating the solutions of an integral equation arising from a problem in mathematical biology

Autor:	Tatjana V. Tomović Mladenović, Maria Carmela De Bonis, Marija P. Stanić
Rok vydání:	2022
Předmět:	Numerical Analysis Mathematical and theoretical biology Smoothness Applied Mathematics Gaussian Lagrange polynomial Stability (learning theory) Integral equation Computational Mathematics symbols.namesake Spline (mathematics) Product (mathematics) symbols Applied mathematics Mathematics
Zdroj:	Applied Numerical Mathematics. 171:193-211
ISSN:	0168-9274
Popis:	The paper deals with an integral equation arising from a problem in mathematical biology. We propose approximating its solution by Nystrom methods based on Gaussian rules and on product integration rules according to the smoothness of the kernel function. In particular, when the latter is weakly singular we propose two Nystrom methods constructed by means of different product formulas. The first one is based on the Lagrange interpolation while the second one is based on discrete spline quasi-interpolants. The stability and the convergence of the proposed methods are proved in uniform spaces of continuous functions. Finally, some numerical tests showing the effectiveness of the methods and the sharpness of the obtained error estimates are given.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::ff5a26c9f8837387a3c7be7e45635f0a https://doi.org/10.1016/j.apnum.2021.09.004 Zobrazit plný text záznamu Full Text from ScienceDirect