Open AccessНовый численный метод решения нелинейных стохастических интегральных уравнений
Author(s) -
Rebiha Zeghdane
Publication year - 2020
Publication title -
vladikavkazskij matematičeskij žurnal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.126
H-Index - 2
eISSN - 1814-0807
pISSN - 1683-3414
DOI - 10.46698/n8076-2608-1378-r
Subject(s) - chebyshev filter , mathematics , algebraic equation , chebyshev nodes , chebyshev polynomials , matrix (chemical analysis) , chebyshev equation , chebyshev iteration , convergence (economics) , integral equation , basis (linear algebra) , basis function , sobolev space , mathematical optimization , mathematical analysis , orthogonal polynomials , nonlinear system , classical orthogonal polynomials , physics , materials science , geometry , quantum mechanics , economics , composite material , economic growth
The purpose of this paper is to propose the Chebyshev cardinal functions for solving Volterra stochastic integral equations. The method is based on expanding the required approximate solution as the element of Chebyshev cardinal functions. Though the way, a new operational matrix of integration is derived for the mentioned basis functions. More precisely, the unknown solution is expanded in terms of the Chebyshev cardinal functions including undetermined coefficients.By substituting the mentioned expansion in the original problem, the operational matrix reducing the stochastic integralequation to system of algebraic equations. The convergence and error analysis of the etablished method are investigated in Sobolev space. The method is numerically evaluated by solving test problems caught from the literature by which the computational efficiency of the method is demonstrated. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by other works and it is efficient to use for different problems.