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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:
65L10Boundary value problems for ODE (numerical methods)
34B05Linear boundary value problems for ODE
46E22Hilbert spaces with reproducing kernels
46B15Summability and bases in normed spaces
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References:
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