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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. © 2012 Copyright Vilnius Gediminas Technical University.

APPROXIMATE SOLUTION OF NONLINEAR MULTI-POINT BOUNDARY VALUE PROBLEM ON THE HALF-LINE