Solutions of integral equations by reproducing kernel hilbert space method

Abstract

The theory of reproducing kernels was considered for the first time at the beginning of the 20th century by Zaremba. Reproducing kernel theory has valuable implementations in numerical analysis, differential equations, probability and statistics. Some authors discussed fractional differential equations, nonlinear oscillators with discontinuity, singular nonlinear two-point periodic boundary value problems and nonlinear partial differential equations by the reproducing kernel Hilbert space method recently. In this chapter, we apply the reproducing kernel Hilbert space method to the integral equations. We give the solutions in the form of a series in the reproducing kernel Hilbert space. We demonstrate some numerical examples to show the accuracy of the technique. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021.