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In this work, we construct a novel weighted reproducing kernel space and give the expression of reproducing kernel function skillfully. Based on the orthogonal basis established in the reproducing kernel space, an efficient algorithm is provided to solve the nonlinear multi-point boundary value problem on the half-line. Uniformly convergence of the approximate solution and convergence estimation of our algorithm are studied. Numerical results show our method has high accuracy and efficiency.

Abstract. In this paper, we construct a complex reproducing kernel space for singular multi-point BVPs, and skillfully obtain reproducing kernel expressions. Then, we transform the problem into an equivalent operator equation, and give a numerical algorithm to provide the approximate solution. The uniform convergence of this algorithm is proved, and complexity analysis is done. Lastly, we show the validity and feasibility of the numerical algorithm by two numerical examples.