TY - JOUR
AU - A.T.Assanova,
AU - E.A.Bakirova,
AU - Zh.M.Kadirbayeva,
PY - 2019/06/10
Y2 - 2024/06/14
TI - NUMERICAL IMPLEMENTATION OF SOLVING A BOUNDARY VALUE PROBLEM FOR A SYSTEM OF LOADED DIFFERENTIAL EQUATIONS WITH PARAMETER
JF - Известия НАН РК. Серия физико-математическая
JA - СФМН
VL -
IS - 3
SE - Статьи
DO -
UR - https://journals.nauka-nanrk.kz/physics-mathematics/article/view/1586
SP - 77-84
AB - <p>A linear two-point boundary value problem for the loaded differential equations with parameter is<br>considered. This problem is investigated by parameterization method. We offer algorithm for solving to boundary<br>value problem for the system of loaded differential equations with parameter. In first, original problem is reduced to<br>equivalent problem consisting the Cauchy problems for system of ordinary differential equations with parameters in<br>subintervals and functional relations with respect to introduced additional parameters. At fixed values of parameters<br>the Cauchy problem for system of ordinary differential equations in subinterval has a unique solution. This solution<br>is represented with fundamental matrix of system. Using these representations we compile a system of linear<br>algebraic equations with respect to parameters. We proposed algorithm for finding of numerical solution to the<br>equivalent problem. This algorithm includes of the numerical solving of the Cauchy problems for system of the<br>ordinary differential equations and solving of the linear system of algebraic equations. For numerical solving of the<br>Cauchy problem we apply the Runge–Kutta method of 4th order. The proposed numerical implementation is<br>illustrated by example.</p>
ER -