Open AccessON THE ALGORITHM FOR SOLVING OF A LINEAR BOUNDARY VALUE PROBLEM FOR ORDINARY DIFFERENTIAL EQUATION WITH PARAMETER
Author(s) -
Н.Б. Искакова,
Zh. Kubanychbekkyzy
Publication year - 2020
Publication title -
habaršy. fizika-matematika seriâsy
Language(s) - English
Resource type - Journals
ISSN - 1728-7901
DOI - 10.51889/2020-2.1728-7901.10
Subject(s) - mathematics , cauchy boundary condition , ordinary differential equation , boundary value problem , initial value problem , cauchy problem , mathematical analysis , uniqueness , exact differential equation , elliptic partial differential equation , exponential integrator , differential equation , free boundary problem , differential algebraic equation
A linear boundary value problem for a system of ordinary differential equations containing a parameter is considered on a bounded segment. For a fixed parameter value, the Cauchy problem for an ordinary differential equation is solved. Using the fundamental matrix of differential part and assuming uniqueness solvability of the Cauchy problem an origin boundary value problem is reduced to the system of linear algebraic equation with respect to unknown parameter. The existence of a solution to this system ensures the existence of a solution to the boundary value problem under study. The algorithm of finding of solution for initial problem is offered based on a construction and solving of the linear algebraic equation. The basic auxiliary problem of algorithm is: the Cauchy problem for ordinary differential equations. The numerical implementation of algorithm offered in the article uses the method of Runge-Kutta of fourth order to solve the Cauchy problem for ordinary differential equations.