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**Solving singular second order three-point boundary value problems using reproducing kernel Hilbert space method.**
*(English)*
Zbl 1178.65085

Summary: This paper investigates the numerical solutions of singular second order three-point boundary value problems using reproducing kernel Hilbert space method. It is a relatively new analytical technique. The solution obtained by using the method takes the form of a convergent series with easily computable components. However, the reproducing kernel Hilbert space method cannot be used directly to solve a singular second order three-point boundary value problem, so we convert it into an equivalent integro-differential equation, which can be solved using reproducing kernel Hilbert space method. Four numerical examples are given to demonstrate the efficiency of the present method. The numerical results demonstrate that the method is quite accurate and efficient for singular second order three-point boundary value problems.

### MSC:

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

34B16 | Singular 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) |

45J05 | Integro-ordinary differential equations |

65R20 | Numerical methods for integral equations |

### Keywords:

nonlinear singular three-point boundary value problem; reproducing kernel Hilbert space method; convergent series; equivalent integro-differential equation; numerical examples
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\textit{F. Geng}, Appl. Math. Comput. 215, No. 6, 2095--2102 (2009; Zbl 1178.65085)

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### References:

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