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arXiv · 1712.01363

On construction of transmutation operators for perturbed Bessel equations

Vladislav V. Kravchenko·Elina L. Shishkina·Sergii M. Torba
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Abstract

A representation for the kernel of the transmutation operator relating the perturbed Bessel equation with the unperturbed one is obtained in the form of a functional series with coefficients calculated by a recurrent integration procedure. New properties of the transmutation kernel are established. A new representation of the regular solution of the perturbed Bessel equation is given presenting a remarkable feature of uniform error bound with respect to the spectral parameter for partial sums of the series. A numerical illustration of application to the solution of Dirichlet spectral problems is presented.

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Vladislav V. Kravchenko, Elina L. Shishkina, Sergii M. Torba. 2017-12-04. On construction of transmutation operators for perturbed Bessel equations. https://arxiv.org/abs/1712.01363

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