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Numerical solution of nonlinear three-point boundary value problem on the positive half-line. (English) Zbl 1252.34021
Summary: We present an efficient numerical algorithm to solve the three-point boundary value problem on the half-line based on the reproducing kernel theorem. Considering the boundary conditions including a limit form, a new weighted reproducing kernel space is established to overcome the difficulty. By applying the reproducing property and the existence of an orthogonal basis in the weighted reproducing kernel space, the approximate solution is constructed by the orthogonal projection of the exact solution. Convergence is also discussed. We demonstrate the accuracy of the method by numerical experiments.
34A45Theoretical approximation of solutions of ODE
34B10Nonlocal and multipoint boundary value problems for ODE
34B40Boundary value problems for ODE on infinite intervals
47B32Operators in reproducing-kernel Hilbert spaces