M. Khaleghi - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
E. Babolian - Faculty of Mathematical Sciences and Computer, Kharazmy University, Tehran, Iran.
S. Abbasbandy - Department of Applied Mathematics, Imam Khomeini International University, Qazvin, ۳۴۱۴۹-۱۶۸۱۸, Iran.

Based on reproducing kernel theory, an effective numerical technique is proposed for solving second order linear two-point boundary value problems with deviating argument. In this method, reproducing kernels with Chebyshev polynomial form are used (C-RKM). The convergence and an error estimation of the method are discussed. The efficiency and the accuracy of the method is demonstrated on some numerical examples.

Two-point boundary value problem, Deviating argument, Polynomial reproducing kernel, Chebyshev polynomials, Chebyshev reproducing kernel method