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Abstract This paper presents a numerical algorithm for solving high-order BVPs. We introduce the construction method of multiscale orthonormal basis in W 2 m [ 0 , 1 ] $W^{m}_{2}[0,1]$ . Based on the orthonormal basis, the numerical solution of the boundary value problem is obtained by finding the ε-approximate solution. In addition, the convergence order, stability, and time complexity of the method are discussed theoretically. At last, several numerical experiments show the feasibility of the proposed method.