Algorithms and Programs for Solving Boundary-Value Problems for Systems of Second-Order ODEs with Piecewise Constant Potentials: Multichannel Scattering and Eigenvalue Problems

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Abstract


The new algorithms and programs, implemented in Maple, for solving waveguide-type multichannel scattering and eigenvalue problems for systems of the second-order ODEs with N х N matrix piecewise constant coefficients on the axis are proposed. New algorithm and program for solving the boundary-value problems by method of matching the fundamental solutions (MMFS) of the system of ODEs at the points of discontinuity of potentials are elaborated. In each of the subintervals of an axis the general solution of the system of ODEs are sought in the form of linear combination of 2N fundamental solutions with unknown coefficients. Each fundamental solution explicitly dependent on spectral parameter and eigenvalues and eigenvectors of algebraic eigenvalue problems with N х N matrix of constant potentials. From the condition of continuity for the solutions and their derivatives at the discontinuity points of the potentials, the system of algebraic equations is followed. In the case of bound or metastable state problem the obtained system of algebraic equations contains nonlinear dependence of unknown spectral parameter. For solving such nonlinear problem symbolic-numerical algorithm is formulated. The benchmark calculations of bound, metastable and scattering states of BVPs for systems of the second-order ODEs obtained using program of the MMFS are compared with those obtained using program of the finite element method.

A A Gusev

Joint Institute for Nuclear Research

Email: gooseff@jinr.ru

O Chuluunbaatar

Joint Institute for Nuclear Research

Email: chuka@jinr.ru

S I Vinitsky

Joint Institute for Nuclear Research

Email: vinitsky@theor.jinr.ru
RUDN University, Moscow, Russia

L L Hai

Joint Institute for Nuclear Research

Email: uonglehai_tcl@yahoo.com.vn
Belgorod State University, Belgorod, Russia

V L Derbov

Saratov State University

Email: derbov@sgu.ru

A Gόźdź

Institute of Physics, University of M. Curie-Sklodowska

Email: andrzej.gozdz@umcs.pl

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Copyright (c) 2016 Гусев А.А., Чулуунбаатар О., Виницкий С.И., Хай Л.Л., Дербов В.Л., Гуждж А.

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