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**A numerical solution to nonlinear second order three-point boundary value problems in the reproducing kernel space.**
*(English)*
Zbl 1246.65122

Summary: A new numerical algorithm is provided to solve nonlinear three-point boundary value problems in a very favorable reproducing kernel space which satisfies all boundary conditions. Its reproducing kernel function is discussed in detail. We also prove that the approximate solution and its first and second order derivatives all converge uniformly. The numerical experiments show that the algorithm is quite accurate and efficient for solving nonlinear second order three-point boundary value problems.

### MSC:

65L10 | Numerical solution of boundary value problems involving ordinary differential equations |

34B15 | Nonlinear boundary value problems for ordinary differential equations |

34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |

46E22 | Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) |

### Keywords:

algorithm; reproducing kernel function; nonlinear three-point boundary value problems; numerical experiments
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\textit{Y. Lin} et al., Appl. Math. Comput. 218, No. 14, 7362--7368 (2012; Zbl 1246.65122)

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