Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8388Research ArticleDescription of a Program for Computing Eigenvalues and Eigenfunctions and Their First Derivatives with Respect to the Parameter of the Coupled Parametric Self-Adjoined Elliptic Differential EquationsGusevA Agooseff@jinr.ruChuluunbaatarOSchool of Mathematics and Computer Sciencechuka@jinr.ruVinitskyS Ivinitsky@theor.jinr.ruAbrashkevichA Gaabrashk@ca.ibm.comJoint Institute for Nuclear ResearchNational University of Mongolia, MongoliaIBM Toronto Lab15022014233634108092016Copyright © 2014,2014Brief description of a FORTRAN 77 program is presented for calculating with the given accuracy eigenvalues, eigenfunctions and their first derivatives with respect to the parameter of the coupled parametric self-adjoined elliptic differential equations with the Dirichlet and/or Neumann type boundary conditions on the finite interval. The original problem is projected to the parametric homogeneous and nonhomogeneous 1D boundary-value problems for a set of ordinary second order differential equations which is solved by the finite element method. The program calculates also potential matrix elements - integrals of the eigenfunctions multiplied by their first derivatives with respect to the parameter. Parametric eigenvalues (so-called potential curves) and matrix elements computed by the POTHEA program can be used for solving the bound state and multi-channel scattering problems for a system of the coupled second-order ordinary differential equations with the help of the KANTBP programs. As a test desk, the program is applied to the calculation of the potential curves and matrix elements of Schr¨odinger equation for a system of three charged particles with zero total angular momentum.boundary value problemfinite element methodKantorovich methodкраевая задачаметод конечных элементовметод Канторовича[A Program Package for Solution of Two-Dimensional Discrete and Continuum Spectra Boundary-Value Problems in Kantorovich (Adiabatic) Approach / O. Chuluunbaatar, A.A. Gusev, S.I. Vinitsky, A.G. Abrashkevich // JINR Lib. - 2013. - http://wwwinfo.jinr.ru/programs/jinrlib/kantbp/indexe.html.][Gusev A.A. The Algorithms of the Numerical Solution to the Parametric Two-Dimensional Boundary-Value Problem and Calculation Derivative of Solution with Respect to the Parameter and Matrix Elements by the Finite-Element Method // Bulletin of PFUR. “Series Mathematics. Information Sciences. Physics”.-2013.- No 1. - Pp. 10-31.][KANTBP 2.0: New Version of a Program for Computing Energy Levels, Reaction Matrix and Radial Wave Functions in the Coupled-Channel Hyperspherical Adiabatic Approach / O. Chuluunbaatar, A.A. Gusev, S.I. Vinitsky, A.G. Abrashkevich // Comput. Phys. Commun. - 2008. - Vol. 179. - Pp. 685-693.][Abrashkevich A.G., Kaschiev M.S., Vinitsky S.I. A New Method for Solving an Eigenvalue Problem for a System of Three Coulomb Particles within the Hyperspherical Adiabatic Representation // J. Comp. Physics. - 2000. - Vol. 163, No 2. - Pp. 328-348.]