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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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