Computational automation for solving Pocklington’s integro-differential equation based on Fredholm integral equations and \(\gamma \)-spline interpolants

Abstract

To solve all types of Fredholm integro-differential equations, we develop a computational automation based on the collocation method. \(\gamma \)-spline basis functions are employed to compute an approximate solution of these linear integral equations. In addition, Pocklington’s integro-differential equation is studied in this work. Accordingly, the signal reconstruction in the wire antennas is treated using these equations. Several techniques based on quadrature computational automation methods are involved to determine the computed solutions of the considered integro-differential equations. Moreover, the \(\gamma \)-spline interpolation function is proposed to solve the Fredholm equation. Some examples are presented to indicate the numerical convergence orders \(\mathcal {O}(h^{\gamma +1})\), accuracy, effectiveness, and robustness of the method.