Reproducing kernel Hilbert space method for nonlinear boundary-value problems. (English) Zbl 1407.34026
Summary: Reproducing kernel Hilbert space method is given for nonlinear boundary-value problems in this paper. Applying this technique, we establish a new algorithm to approximate the solution of such nonlinear boundary-value problems. This technique does not need any background mesh and can easily be applied. In this technique, the solution is given in the form of a series. Representation of the solutions is obtained in the reproducing kernel Hilbert space. Additionally, the convergence of the presented method is demonstrated. Numerical examples are presented to show the ability of the method. We compare the reproducing kernel Hilbert space method with B-spline collocation method. As seen in the tables, the reproducing kernel Hilbert space method gives better results.
MSC:
| 34A45 | Theoretical approximation of solutions to ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 34A25 | Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. |
Keywords:
nonlinear boundary-value problems; reproducing kernel Hilbert space method; series solutionsReferences:
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