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Mathematical Methods in the Applied Sciences
ISSN
0170-4214
1099-1476
Издатель
Wiley
4 результаты
Показано: 1 - 4 из 4
- Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, CMMSE: Numerical Method for Solving Problem for Delay Integro‐Differential EquationABSTRACT The object of interests of this paper is the two‐point linear boundary value problem for a delay Fredholm integro–differential equation. To solve this problem numerically, a Dzhumabaev parameterization method is presented, which is based on the dividing the given interval into subintervals and introducing additional parameters, which enables to transform the given problem into a respective system of algebraic equations. Numerical illustrations confirm our theoretical analysis. - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, Numerical Solution of Second‐Order Impulsive Differential Equations With Loadings Subject to Integral Boundary ConditionsABSTRACT In this paper, we present a computational method for solving the second‐order impulsive differential equations with loadings subject to integral boundary conditions based on the Dzhumabaev parametrization method. The idea of this method involves introducing additional parameters, reducing the original problem to solving a system of linear algebraic equations. The system's coefficients and right‐hand side are determined by solving Cauchy problems for ODEs and by calculating definite integrals. Four examples are provided to show the effectiveness and feasibility of the main results.Цитирования (OpenAlex) 9Цитирования (OpenCitations) 6 - 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, 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