Mixed reproducing kernel-based iterative approach for nonlinear boundary value problems with nonlocal conditions

In this paper, a mixed reproducing kernel function (RKF) is introduced. The kernel function consists of piecewise polynomial kernels and polynomial kernels. On the basis of the mixed RKF, a new numerical technique is put forward for solving nonlinear boundary value problems (BVPs) with nonlocal conditions. Compared with the classical RKF-based methods, our method is simpler since it is unnecessary to convert the original equation to an equivalent equation with homogeneous boundary conditions. Also, it is not required to satisfy the homogeneous boundary conditions for the used RKF. Finally, the higher accuracy of the method is shown via several numerical tests.