Application of reproducing kernel method to third order three-point boundary value problems.(English)Zbl 1204.65090

Summary: We investigate the analytical approximate solutions of third order three-point boundary value problems using the reproducing kernel method. The solution obtained by using the method takes the form of a convergent series with easily computable components. However, the reproducing kernel method can not be used directly to solve third order three-point boundary value problems, since there is no method of obtaining reproducing kernel satisfying three-point boundary conditions.
This paper presents a method for solving reproducing kernel satisfying three-point boundary conditions so that reproducing kernel method can be used to solve third order three-point boundary value problems. Results of numerical examples 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 34B05 Linear boundary value problems for ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
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References:

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