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Zbl 1178.65085
Geng, Fazhan
Solving singular second order three-point boundary value problems using reproducing kernel Hilbert space method. (English)
[J] Appl. Math. Comput. 215, No. 6, 2095-2102 (2009). ISSN 0096-3003

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 2000:: *65L10 Boundary value problems for ODE (numerical methods)
34B16 Singular nonlinear boundary value problems
34B10 Multipoint boundary value problems
46E22 Hilbert spaces with reproducing kernels
45J05 Integro-ordinary differential equations
65R20 Integral equations (numerical methods)

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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Zentralblatt MATH Berlin [Germany]