A matrix method for system of integro-differential equations by using generalized Laguerre polynomials

• Main Authors: Mashallah Matinfar, Abbas Riahifar
• Format: Article
• Language: English
• Published: Ferdowsi University of Mashhad 2016-09-01
• Series: Iranian Journal of Numerical Analysis and Optimization
• Subjects: systems of linear fredholm integro-dierential equations; un- bounded domain; generalized laguerre polynomials; operational matrix of integration
• Online Access: https://ijnao.um.ac.ir/article_24491_3000d6e1f047f1c6749d7c4435309721.pdf

The purpose of this research is to present a matrix method for solving system of linear Fredholm integro-differential equations(FIDEs) of the second kind on unbounded domain with degenerate kernels in terms of generalized Laguerre polynomials(GLPs). The method is based on the approximation of the truncated generalized Laguerre series. Then the system of (FIDEs) along with initial conditions are transformed into the matrix equations, which corresponds to a system of linear algebraic equations with the unknown generalized Laguerre coefficients. Combining these matrix equations and then olving the system yields the generalized Laguerre coefficients of the solution function. In addition, several numerical examples are given to demonstrate the validity, efficiency and applicability of the technique.