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**A numerical solution to nonlinear multi-point boundary value problems in the reproducing kernel space.**
*(English)*
Zbl 1206.65187

Summary: A new numerical algorithm is provided to solve nonlinear multi-point boundary value problems in a very favorable reproducing kernel space, which satisfies all complex boundary conditions. Its reproducing kernel function is discussed in detail. The theorem proves 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 multi-point boundary value problems.

### MSC:

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

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

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

65L20 | Stability and convergence of numerical methods for ordinary differential equations |

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

### Keywords:

nonlinear problems; multi-point boundary value conditions; reproducing kernel space; convergence; algorithm; numerical experiments
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\textit{Y. Lin} and \textit{M. Cui}, Math. Methods Appl. Sci. 34, No. 1, 44--47 (2011; Zbl 1206.65187)

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### References:

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