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Zbl 1149.65057
Cui, Minggen; Geng, Fazhan
Solving singular two-point boundary value problem in reproducing kernel space. (English)
[J] J. Comput. Appl. Math. 205, No. 1, 6-15 (2007). ISSN 0377-0427

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.
[Raytcho D. Lazarov (College Station)]

MSC 2000:: *65L10 Boundary value problems for ODE (numerical methods)
34K10 Boundary value problems for functional-differential equations
34B05 Linear boundary value problems of ODE
46E22 Hilbert spaces with reproducing kernels
47B32 Operators in reproducing-kernel Hilbert spaces
34K28 Numerical approximation of solutions of FDE

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

Cited in: Zbl 1162.34346

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