International Journal of Mathematics and Physics

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Numerical solution of a control problem for ordinary differential equations with multipoint integral condition
(Al-Farabi Kazakh National University, 2019-12-20)
A. T. Assanova
;
E. А. Bakirova
;
Zh. М. Каdirbayeva
A linear boundary value problem with a parameter for ordinary differential equations with multipoint integral conditionis investigated.The method of parameterization is used for solving the considered problem. The linear boundary value problem with a parameter for ordinary differential equations with multipoint integral condition by introducing additional parameters at the partition points is reduced to equivalent boundary value problem with parameters. The equivalent boundary value problem with parameters consists of the Cauchy problem for the system of ordinary differential equations with parameters, multipoint integral condition and continuity conditions. The solution of the Cauchy problem for the system of ordinary differential equations with parameters is constructed using the fundamental matrix of differential equation. The system of linear algebraic equations with respect to the parameters are composed by substituting the values of the corresponding points in the built solutions to the multipoint integral condition and the continuity condition. Numerical method for finding solution of the problem is suggested, which based on the solving the constructed system and Runge-Kutta method of the 4-th order for solving Cauchy problem on the subintervals.
Цитирования (OpenAlex) 6Цитирования (OpenCitations) 2
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A novel numerical implementation for solving problem for loaded DEPCAG
(Al-Farabi Kazakh National University, 2023-01-10)
Zh. М. Каdirbayeva
;
Roza E. Uteshova
;
G. Marat
;
B. B. Мinglibayeva
In this work, we propose a new computational approach is implemented to solve a two-point BVP for a loaded differential equation with piecewise constant argument of generalized type (DEPCAG) based on the Dzhumabaev parameterization method. In this method, as parameters, we take the values of the desired solution at the partition points which are chosen taking into account the specifics of the equation. The problem under consideration reduces to an equivalent parametric problem for ordinary differential equations. A solution to this problem, which in turn are found from a system of linear algebraic equations. The found values of the parameters are used to determine the values of the unknown function at the remaining points of the interval by solving auxiliary initial-value problems. We develop a novel numerical implementation for solving the considered a two-point BVP for loaded DEPCAG and provide two examples illustrating its application, where Mathcad software will be used for the calculation.
Цитирования (OpenAlex) 8Цитирования (OpenCitations) 7

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