In this study a reproducing kernel Hilbert space method with Chebyshev
function is proposed for approximating solutions of a nonlinear system
of ordinary differential equations under multi-point boundary
conditions. Based on reproducing kernel theory, reproducing kernel
functions with a polynomial form will be erected in the reproducing
kernel spaces spanned by the shifted Chebyshev polynomials. Convergence
analysis of the proposed technique is theoretically investigated. This
approach is successfully used for solving a system of ordinary
differential equations with multi-point boundary conditions arising in
flow of an electrically conducting nanofluid over an impermeable
stretching cylinder.