A Collocation Method for Solving System of Volterra-differential-difference Equations with Terms of Chebyshev Polynomials
Yalçın Öztürk *
Ula Ali Koçman Vocational School, Muğla Sıtkı Koçman University, Muğla, Turkey
Mustafa Gülsu
Department of Mathematics, Faculty of Science, Muğla Sıtkı Koçman University, Muğla, Turkey
*Author to whom correspondence should be addressed.
Abstract
In this study, we present a numerical algorithm for solving systems of Volterra-differential-difference equations with variable coefficients by collocation method. This algorithm based on polynomial approximation, using the first kind Chebyshev polynomial basis with collocation method. This method transforms the system of Volterra-differential-difference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. In addition, convergence analysis of the method is presented. Some cases of the mentioned equations are solved as examples to illustrate the reliability of the method. The results reveal that the method is very effective and accuracy.
Keywords: Systems of Volterra-differential-difference equations, collocation method, approximation method, error estimation, Chebyshev polynomials