Solving singular two-point boundary value problem in reproducing kernel space. (English) Zbl 1149.65057

Cui, Minggen; Geng, Fazhan

J. Comput. Appl. Math. 205, No. 1, 6-15 (2007).

Authors’ summary: We present a new method for solving singular two-point boundary value problem for certain ordinary differential equation having singular coefficients. Its exact solution is represented in the form of series in reproducing kernel space. In the mean time, the \(n\)-term approximation \(u_{n}(x)\) to the exact solution \(u(x)\) is obtained and is proved to converge to the exact solution. Some numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method are compared with the exact solution of each example and are found to be in good agreement with each other.

Reviewer: Raytcho D. Lazarov (College Station)

MSC:

65L10	Numerical solution of boundary value problems involving ordinary differential equations
34K10	Boundary value problems for functional-differential equations
34B05	Linear 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)
47B32	Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)
34K28	Numerical approximation of solutions of functional-differential equations (MSC2010)

Keywords:

exact solution; singular two-point value boundary problem; reproducing kernel

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