Abstract
A numerical scheme has been developed for solving the system of linear Fredholm integro-differential equations subject to the mixed conditions using Laguerre polynomials. Using collocation method, the system of Fredholm integro-differential equations has been transformed to the system of linear equations in unknown Laguerre coefficients, which leads to the solution in terms of Laguerre polynomials. Moreover, the accuracy and applicability of the scheme have been compared with Tau method and Adomian decomposition method that reveals the proposed scheme to be more efficient.
Highlights
There are many branches of science, such as control theory and financial mathematics, which leads to integro-differential equations (IDEs)
A numerical scheme has been developed for solving the system of linear Fredholm integro-differential equations subject to the mixed conditions using Laguerre polynomials
The system of Fredholm integro-differential equations has been transformed to the system of linear equations in unknown Laguerre coefficients, which leads to the solution in terms of Laguerre polynomials
Summary
There are many branches of science, such as control theory and financial mathematics, which leads to integro-differential equations (IDEs). IDEs mostly occur in many applied areas including engineering, physics and biology [1,2,3,4,5,6]. The resolution of many problems in physics and engineering leads to differential and integral equations in bounded or unbounded domains. In the fields of applied mathematics and scientific computing, spectral methods [8,9,10] became popular among researchers as a robust numerical tool. The remarkable results are obtained, using the spectral methods, to solve the problems [11,12,13] in different fields of natural sciences.
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