Saeid Abbasbandy - Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin ۳۴۱۴۹-۱۶۸۱۸, Iran.
Hussein Sahihi - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Tofigh Allahviranloo - Bahcesehir University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey.

In this paper, a reliable new scheme is presented based on combining Reproducing Kernel Method (RKM) with a practical technique for the nonlinear problem to solve the System of Singularly Perturbed Boundary Value Problems (SSPBVP). The Gram-Schmidt orthogonalization process is removed in the present RKM. However, we provide error estimation for the approximate solution and its derivative. Based on the present algorithm in this paper, can also solve linear problem. Several numerical examples demonstrate that the present algorithm does have higher precision.

Reproducing kernel method, Singularly perturbed BVPs, Convergence analysis, Error analysis, System of differential equations