Қазақ ұлттық қыздар педагогикалық университеті / Казахский национальный женский педагогический университет
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Тип записи:Публикация, NUMERICAL SOLUTION OF A BOUNDARY VALUE PROBLEM WITH A PARAMETER FOR IMPULSIVE LOADED DIFFERENTIAL EQUATIONS(2024-07-01); ; The boundary value problem depending on the parameter for the system of impulsive loaded differential equations is considered. Algorithms of numerical realization of the Dzhumabaev parameterization method are developed for numerical solving of the studied boundary value problem depending on the parameter. Algorithms of numerical realization of the Dzhumabaev parameterization method are based on the solving of Cauchy problems for the system of ordinary differential equations. As a result of application of the proposed method, finding a solution to the boundary value problem depending on the parameter for impulsive loaded differential equations leads to finding a solution to the system of algebraic equations. This system of algebraic equations consists of a boundary condition and equalities with respect to the conditions at the impulsive points. Numerical results showing the high efficiency of the numerical implementation of the Dzhumabaev parameterization method are given. The result demonstrate that there is congruence between the numerical and the exact results to a high order of accuracy. - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, CMMSE: Solving Impulsive Boundary Value Problem for Nonlinear Differential Equations With ParameterABSTRACT This paper is devoted to the study of a two‐point impulsive boundary value problem for a system of nonlinear first‐order ordinary differential equations involving an unknown parameter appearing in both the differential equation and the boundary condition. The main objective is to establish sufficient conditions for the existence of an isolated solution within some set. To achieve this, we apply the Dzhumabaev parametrization method. Based on this approach, we develop a constructive algorithm for finding the solution. The method effectively addresses the discontinuities introduced by the impulses and ensures solvability under clearly defined conditions. A numerical example is presented to illustrate the efficiency and practical applicability of the proposed algorithm. The results demonstrate the method's potential for solving a wide range of nonlinear impulsive boundary value problems with parameters.Цитирования (OpenAlex) 1 - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, Analysis of Semi-periodic Problem for Integro-differential Equations of Parabolic TypeAbstract In this paper, we investigate a semi-periodic boundary-value problem for parabolic integro-differential equations. To solving this problem, we employ spatial discretization via the method of lines, which transforms the continuous formulation into a discrete one. The resulting system is then treated by means of Dzhumabaev’s parameterization technique, reducing it to an equivalent Cauchy-type problem for a system of Fredholm integro-differential equations with periodic and continuity conditions imposed at the partition points. The construction of the solution relies on the fundamental matrix. Theoretical results are established to clarify the relationship between the original integro-differential formulation and its discretized counterpart. A numerical algorithm is further developed, which involves solving the auxiliary system, applying the classical fourth-order Runge-Kutta method to the Cauchy problems on subintervals, and employing Simpson’s rule to approximate definite integrals. Numerical experiments on test problems demonstrate both the accuracy and efficiency of the proposed approach. - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, Application of the Parameterization Method to Nonlinear Boundary Value Problem With a Nonfixed Moment of Impulsive ActionABSTRACT This paper investigates a nonlinear boundary value problem for a system of linear differential equations with a nonfixed moment of impulsive action. To address this problem, we apply the Dzhumabaev parameterization method, which is adapted to account for the nonlinearity of the boundary conditions and the presence of an unknown impulsive moment. These features required modifications of the classical schemes of the method, leading to the development of new algorithms that incorporate the non‐fixed impulsive action. The main contribution of this work is the extension of the applicability of the parameterization method and the derivation of solvability conditions for the problem under consideration. To illustrate the theoretical results, an example is presented.Цитирования (OpenAlex) 1Цитирования (OpenCitations) 1