RELATIONSHIPS BETWEEN VOLTERRA'S INTEGRAL EQUATIONS AND LINEAR SECOND-ORDER DIFFERENTIAL EQUATIONS

Authors

  • Zulpukarov Zhakshylyk Alibaevich Osh Technological University
  • Abdulla kyzy Elnura Osh State Pedagogical University named after A. Zh. Myrsabekov
  • Abdimitalip kyzy Aida Osh State Pedagogical University named after A. Zh. Myrsabekov

DOI:

https://doi.org/10.56122/..v2i2%20(26).404

Keywords:

Математикалык анализ, функционалдык роль, практикалык колдонуу, дифференциалдык теңдемелер, интегралдык эсептөөлөр, экономикалык моделдер, система динамикасы, оптимизациялык маселелер.

Abstract

This article discusses the relationship between linear homogeneous and inhomogeneous second-order differential equations and Volterra integral equations of the first and second kind with examples. On the contrary, a method is provided for reducing simple homogeneous and inhomogeneous linear second-order differential equations to Volterra integral equations of the first and second kind. It allows you to solve, numerically solve, approximate solve, and graph examples of linear homogeneous and inhomogeneous second-order differential equations using the dsolve command in Maple. The solution of Volterra integral equations of the first and second kind satisfies the theorem on uniqueness and existence at points that do not have singularities in the Cauchy problem.

Key words: differential equation, integral equations, derivative, initial condition, Cauchy problem.

References

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Краснов М.Л., Киселев А.И., Макаренко Г.И. Интегральные уравнения. М.: Наука, 1976.

Попов В.А. Сборник задач по интегральным уравнениям. Казань: КГУ, 2006.

Савотченко С.Е., Кузьмичева Т.Г. Методы решения математических задач в Maple: Учебное пособие – Белгород: Изд. Белаудит, 2001. – 116 с.

Зулпукаров Ж. А., Рахматдула уулу Т., Эгемберди кызы Г. Построение функции Грина для дифференциальных уравнений второго порядка с однородными краевыми условиями ОшТУ Известия 2025.–С. 160-166. elibrary_80543046_68953683.pdf

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Published

2025-11-11

How to Cite

Zulpukarov , Z., Abdulla kyzy, E., & Abdimitalip kyzy, A. (2025). RELATIONSHIPS BETWEEN VOLTERRA’S INTEGRAL EQUATIONS AND LINEAR SECOND-ORDER DIFFERENTIAL EQUATIONS. Bulletin of the Osh State Pedagogical University Named After A. Myrsabekova, 2(2 (26), 106–113. https://doi.org/10.56122/.v2i2 (26).404

Issue

Vol. 2 No. 2 (26) (2025): Bulletin of the Osh State Pedagogical University named after A. Myrsabekova

Section

Physical and Mathematical Sciences

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