A Method for Solving a Multipoint BVP With a Nonlinear Integro-Differential Operator
Mynbayeva S.
30 March 2026John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2026#49Issue 54611 - 4621 pp.
The study examines the applicability of the Dzhumabaev parametrization method to multipoint boundary value problems for a Duffing-type integro-differential operator equation. The original problem is reformulated as an equivalent parametric multipoint problem, which was then decomposed into two subproblems: A nonlinear special Cauchy problem and a system of nonlinear algebraic equations. The special Cauchy problem is addressed via linearization at fixed parameter values and solved through a sequence of stepwise linear approximations. The solutions obtained are subsequently employed to construct the right-hand side of the algebraic system and its associated Jacobi matrix. On this basis, a new approach for solving the original problem is developed. The efficiency and convergence of the proposed approach were confirmed through a numerical example.
Duffing-type integro-differential equation , iterative process , multipoint boundary value problem , parametrization method
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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
K. Zhubanov Aktobe Regional University, Aktobe, Kazakhstan
Institute of Mathematics and Mathematical Modeling
K. Zhubanov Aktobe Regional University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026