In this paper, we propose a unified reproducing kernel collocation method(RKCM) for solving boundary value problems of arbitrary order m. For the m-order differential equation, we construct basis functions based on the reproducing kernel function in the \(W_2^m\) space. Additionally, within each subdivision unit, we select m Gaussian points as collocation points. Our method exhibits optimal convergence orders, specifically, the convergence orders under the \(L^\infty ,L^2,H^1,H^2\) error norms are \(2m,2m,2m-1\) and \(2m-2\) respectively, which show significantly higher efficiency compared to existing reproducing kernel methods. Moreover, we also observe a superconvergence phenomenon, where the convergence order under the \(\Vert \cdot \Vert _{\mathcal {L}}\) -average error reaches 2m. Computational experiments substantiate the stability and convergence of the suggested numerical method.
