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)8708Algorithm of Numerical Solving the Parametric Sturm-Liouville Problem and Calculation of Solution Derivatives with Respect to the Parameter via the Finite-Element MethodChuluunbaatarOJoint Institute for Nuclear Research-Joint Institute for Nuclear Research150220092546508092016Copyright © 2009,2009The economical algorithm is presented for numerical solving with the given accuracy of the parametrical Sturm-Liouville problem with the third type boundary conditions on the finite interval by the finite-element method with automatical shift of the spectrum. The algorithm includes the calculation with given accuracy a set ∼ 10-50 of the eigenvalues, eigenfunctions and their first derivatives with respect to the parameter, and integrals - matrix elements between eigenfunctions and their derivatives with respect to the parameter. Efficiency of the algorithm is demonstrated by numerical analysis of the parametric integrable problem with the parametric third type boundary conditions.параметрическая задача Штурма-Лиувилляметод конечных элементовметод Канторовича