A Specific Numerical Method for Two-Dimensional Linear Fredholm Integral Equations of the Second Kind by Boubaker Polynomial Bases

In this paper, we introduce a new collocation method, based on Boubaker polynomials, for approximate solutions of a class of two-dimensional Fredholm linear integral equations of the second kind. The properties of the two-dimensional Boubaker functions are used. The basic integration matrix is used by collocation points to reduce the answer form of the integral equation to the answer form of the algebraic equation system. The accuracy of the answer and error analysis has been studied thoroughly and structurally, and it has been emphasized that the proposed method for a variety of two-dimensional integral equations of linear Fredholm with a continuous kernel is an entirely accurate and error-free polynomial type. Moreover, the error estimation of the approximate solution and exact solution are also provided. Numerical examples are presented to illustrate and compare the results of the truncated Boubaker collocation method with the results of other methodologies to provide validity, capability and efficiency of the technique. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.