ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

On Modified Spline Collocations Method for Solving the Fredholm Integral Equation


Egor K. Kulikov

St. Petersburg State University
Department of Parallel Algorithms
Post-graduate student
Russia, 199034, Saint-Petersburg, Universitetskaya nab., 7/9

Anton A. Makarov

St. Petersburg State University
Department of Parallel Algorithms
Professor, Dr. Sci., docent
Russia, 199034, Saint-Petersburg, Universitetskaya nab., 7/9


A numerical method to solve a Fredholm integral equation of the second kind is studied. This approach is based on a collocation method and Sloan iterations. Our solution is represented by a linear combination of minimal splines, and the coefficients are calculated by a method of local approximation (quasi-interpolation). The results of numerical experiments demonstrating how the quality of approximation can be improved by using minimal trigonometric splines and corresponding functionals in comparison with several earlier suggested approaches are presented.



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