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

65L10Boundary value problems for ODE (numerical methods)
34K10Boundary value problems for functional-differential equations
34B05Linear boundary value problems for ODE
46E22Hilbert spaces with reproducing kernels
47B32Operators in reproducing-kernel Hilbert spaces
34K28Numerical approximation of solutions of functional-differential equations
Full Text: DOI
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