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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:
65L10Boundary value problems for ODE (numerical methods)
34B16Singular nonlinear boundary value problems for ODE
34B10Nonlocal and multipoint boundary value problems for ODE
46E22Hilbert spaces with reproducing kernels
45J05Integro-ordinary differential equations
65R20Integral equations (numerical methods)
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