In this work, we consider system of linear and nonlinear Volterra integral equations (VIEs) of the first kind. At first, we have converted system of VIEs of the first kind to an equation of the second kind by differentiation of transformation. Then standard Adomian decomposition method (ADM) and modified ADM (MADM) are used to find semi-analytical solution. The Adomian decomposition method converts Volterra integral equations of the second kind into determination of computable components of iterative integral equations. The uniqueness solutions of the system of nonlinear VIEs of the second kind are proved and the choice of the initial data is shown. It is practically shown that the obtained series by MADM convergence very rapidly to the exact solution. Finally, four examples were illustrated to show validity and applicability of this approach. The examples are taken from the works mentioned in the references.
| Mualliflar | Eshkuvatov, Z.K., Salimova, N.M., Khudoyberganov, M.O., Эшкуватов, З.К., Салимова, Н.М., Худойберганов, М.О. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashriyot | Тошкент ахборот технологиялари университети қошидаги, Ахборот-коммуникация технологиялари илмий-инновацион, маркази |
| ISSN | 2181-8460, 2181-046X |
| Nashr sanasi | 2024-12-11 |
| Son | 4/1 |
| Betlar | 23-36 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| Indeksga qo‘shilgan | 2026-08-27 |
Volterra integral equation, Adomian decomposition method, Semi-analytical solution, интегральное уравнение Вольтерра, метод разложения Адомиана, полуаналитическое решение
| APA | Eshkuvatov, Z.K., Salimova, N.M., Khudoyberganov, M.O., Эшкуватов, З.К., Салимова, Н.М., & Худойберганов, М.О. (2024). Solving system of Volterra integral equations of the first kind by modified Adomian decomposition method. Ҳисоблаш ва амалий математика муаммолари, (4/1), 23-36. https://journals.airi.uz/index.php/pvpm/article/view/45 |
|---|---|
| GOST (OAK) | Eshkuvatov, Z.K. va b. Solving system of Volterra integral equations of the first kind by modified Adomian decomposition method // Ҳисоблаш ва амалий математика муаммолари. – 2024. – № 4/1. – P. 23-36. |
| MLA | Eshkuvatov, Z.K., Salimova, N.M., Khudoyberganov, M.O., Эшкуватов, З.К., Салимова, Н.М., and Худойберганов, М.О. “Solving system of Volterra integral equations of the first kind by modified Adomian decomposition method.” Ҳисоблаш ва амалий математика муаммолари, (4/1), 23-36, 2024. https://journals.airi.uz/index.php/pvpm/article/view/45 |
| Chicago | Eshkuvatov, Z.K., Salimova, N.M., Khudoyberganov, M.O., Эшкуватов, З.К., Салимова, Н.М., and Худойберганов, М.О. “Solving system of Volterra integral equations of the first kind by modified Adomian decomposition method.” Ҳисоблаш ва амалий математика муаммолари, (4/1), 23-36 (2024). https://journals.airi.uz/index.php/pvpm/article/view/45 |
| Harvard | Eshkuvatov, Z.K., Salimova, N.M., Khudoyberganov, M.O., Эшкуватов, З.К., Салимова, Н.М., and Худойберганов, М.О (2024) ‘Solving system of Volterra integral equations of the first kind by modified Adomian decomposition method’, Ҳисоблаш ва амалий математика муаммолари, (4/1), 23-36. https://journals.airi.uz/index.php/pvpm/article/view/45 |
| BibTeX | @article{eshkuvatovzk2024,
title = {Solving system of Volterra integral equations of the first kind by modified Adomian decomposition method},
author = {Eshkuvatov, Z.K. and Salimova, N.M. and Khudoyberganov, M.O. and Эшкуватов, З.К. and Салимова, Н.М. and Худойберганов, М.О.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2024},
number = {4/1},
pages = {23-36},
url = {https://journals.airi.uz/index.php/pvpm/article/view/45}
} |
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