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A new method for solving a class of singular two-point boundary value problems. (English) Zbl 1161.65060
A solution for the two-point boundary value problem
$Lu\equiv u^{\prime\prime}(x)+(k/x)u^{\prime}(x)+b(x)u(x) =f(x)$ with conditions $$u\prime(0)=0, u(1)= 1$$ is presented in form of a series in the special space $$W=W_{2}^{3}[0,1]$$, named reproducing kernel space. The construction of an orthonormal system in $$W$$ uses the adjoint operator $$L^{*}$$, that is why not simple. This approximate method has an analytical form , but is not numerical.

##### MSC:
 65L10 Numerical solution of boundary value problems involving ordinary 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) 46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
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