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Numerical solution of nonlinear three‐point boundary value problem on the positive half‐line
Author(s) -
Niu J.,
Lin Y. Z.,
Zhang C. P.
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2549
Subject(s) - mathematics , kernel (algebra) , boundary value problem , convergence (economics) , limit (mathematics) , mathematical analysis , projection (relational algebra) , orthographic projection , space (punctuation) , nonlinear system , kernel method , algorithm , geometry , pure mathematics , computer science , physics , quantum mechanics , artificial intelligence , support vector machine , economics , economic growth , operating system
In this paper, 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 reproducing property and existence of the orthogonal basis in the weighted reproducing kernel space, the approximate solution is constructed by the orthogonal projection of the exact solution. Convergence has also been discussed. We demonstrate the accuracy of the method by numerical experiments. Copyright © 2012 John Wiley & Sons, Ltd.