Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia8565Research ArticleAlgorithm for Solving the Two-Dimensional Boundary Value Problem for Model of Quantum Tunneling of a Diatomic Molecule Through Repulsive BarriersGusevA ALaboratory of Information Technologiesgooseff@jinr.ruHaiLuong Leluonglehai_tcl@yahoo.com.vnJoint Institute for Nuclear ResearchBelgorod State National Research University150120151153608092016Copyright © 2015,2015Algorithm for solving the boundary value problems that describe the model of quantum tunneling of a diatomic molecule through repulsive barriers in s-wave approximation is presented. The boundary value problems are formulated and reduced to the one-dimensional ones for systems of coupled second-order differential equations by means of the Galerkin and Kantorovich methods. The description of elaborated algorithms and the calculated asymptotes of parametric basis functions, matrices of variable coefficients, and fundamental solutions of the systems of the coupled second-order differential equations needed for solving the boundary problems on a finite interval are given. The BVPs were solved by the elaborated set of programs implementing the finite element method. Analysis of benchmark calculations of quantum tunneling of a diatomic molecule model with the nuclei coupled by the Morse potential through Gaussian barriers and quantum transparency effect induced by metastable states embedded in continuous spectrum below dissociation threshold are presented.quantum tunneling problemdiatomic moleculerepulsive barriersboundary-value problemsGalerkin methodKantorovich methodasymptotic solutionsfinite element methodквантовое туннелированиедвухатомные молекулыотталкивающие барьерыкраевые задачиметод Галёркинаметод Канторовичаасимптотические решенияметод конечных элементов