Nonlinear second order systems of Fredholm integro-differential equations

A large class of physical phenomena in biophysics, chemical engineering, and physical sciences are modeled as systems of Fredhold integro-differential equations. In its simplest form, such systems are linear and analytic solutions might be obtained in some cases while numerical methods can be also used to solve such systems when analytic solutions are not possible. For more realistic and accurate study of underlying physical behavior, including nonlinear actions is useful. In this paper, we use the Chebyshev pseudo-spectral method to solve the pattern nonlinear second order systems of Fredholm integro-differential equations. The method reduces the operators to a nonlinear system of equations that can be solved alliteratively. The method is tested against the reproducing kernel Hilbert space (RKHS) method and shows good performance. The present method is easy to implement and yields very good accuracy for using a relatively small number of collocation points. © 2021, The Author(s), under exclusive licence to Sociedad Española de Matemática Aplicada.