- - - School of Mathematics and Statistics, University of South Florida, Tampa, Florida ۳۳۶۲۰, USA.
- - - School of Mathematics and Statistics, Changshu Institute of Technology, Suzhou, Jiangsu ۲۱۵۵۰۰, China.
- - - School of Mathematical Sciences, Harbin Institute of Technology, Harbin, Heilongjiang ۱۵۰۰۰۱, China.

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 non-linear 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.

Reproducing kernel method, Nonlocal conditions, Iterative methods