دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات45
تعداد شماره‌ها1,501
تعداد مقالات18,365
تعداد مشاهده مقاله59,576,468
تعداد دریافت فایل اصل مقاله20,846,996
Aghaei Amirkhizi, Simin, Mahmoudi, Yaghoub, Salimi shamloo, Ali. (1403). Solution of Volterra integral equations of the first kind with discontinuous kernels by using the Adomian decomposition method. سامانه مدیریت نشریات علمی, 12(1), 189-195. doi: 10.22034/cmde.2023.52806.2227
Simin Aghaei Amirkhizi; Yaghoub Mahmoudi; Ali Salimi shamloo. "Solution of Volterra integral equations of the first kind with discontinuous kernels by using the Adomian decomposition method". سامانه مدیریت نشریات علمی, 12, 1, 1403, 189-195. doi: 10.22034/cmde.2023.52806.2227
Aghaei Amirkhizi, Simin, Mahmoudi, Yaghoub, Salimi shamloo, Ali. (1403). 'Solution of Volterra integral equations of the first kind with discontinuous kernels by using the Adomian decomposition method', سامانه مدیریت نشریات علمی, 12(1), pp. 189-195. doi: 10.22034/cmde.2023.52806.2227
Aghaei Amirkhizi, Simin, Mahmoudi, Yaghoub, Salimi shamloo, Ali. Solution of Volterra integral equations of the first kind with discontinuous kernels by using the Adomian decomposition method. سامانه مدیریت نشریات علمی, 1403; 12(1): 189-195. doi: 10.22034/cmde.2023.52806.2227

Solution of Volterra integral equations of the first kind with discontinuous kernels by using the Adomian decomposition method

Computational Methods for Differential Equations
مقاله 15، دوره 12، شماره 1، فروردین 2024، صفحه 189-195    اصل مقاله (282.12 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.52806.2227
نویسندگان
Simin Aghaei Amirkhizi1؛ Yaghoub Mahmoudi* 2؛ Ali Salimi shamloo3
1Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran
2Department of Mathematics, Tabriz Branch Islamic Azad University, Tabriz, Iran
3Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran
چکیده
In this paper, for solving linear and nonlinear Volterra integral equations of the first kind with discontinuous kernels, the Adomian decomposition method, and the modified Adomian decomposition method are presented. We convert  the  main equation into the  Volterra integral equation of the second kind. The numerical examples are given to denote the accuracy of the suggested method.
کلیدواژه‌ها
Volterra integral equation؛ Piecewise continuous kernel؛ Modified Adomian decomposition method
مراجع
  • [1] S. Aghaei Amirkhizi, Y. Mahmoudi, and A. Salimi Shamloo, Legendre polynomials approximation method for solving Volterra integral equations of the first kind with discontinuous kernels, Indian J. Pure Appl. Math., 53 (2022) 492-504.
  • [2] P. M. Anselone, Uniform approximation theory for integral equations with discontinuous kernels, SIAM J. Numer. Anal., 4 (1967), 245–253.
  • [3] I. L. El-kalla, Convergence of Adomian’s method applied to a class of Volterra type integro-differential equations, Int. J. Differ. Equ. Appl., 10 (2005), 225–234.
  • [4] N. Hritonenko and Y. Yatsenko, Mathematical modeling in economics, ecology and the environment, 2nd Edition, Springer 2013.
  • [5] C. Kasumo and E. Moyo, Approximate solutions of nonlinear Volterra integral equations of the first kind, Appl. Math. Sci., 14 (2020), 867-880.
  • [6] A. P. Khromov, Integral operators with discontinuous kernels, Doklady Akademii Nauk, 406 (2006), 317–321.
  • [7] I. R. Muftahov and D. N. Sidorov, and numerical solutions of systems of nonlinear Volterra integral equations of the first kind with piecewise continuous kernels, Bulletin of the South Ural State University. Series-Mathematical Modelling, Programming and Computer Software, 9 (2016), 130-136.
  • [8] I. Muftahov, A. Tynda, and D. Sidorov, Numeric solution of Volterra integral equations of the first kind with discontinuous kernels, J. Comput. Appl. Math., 313 (2017), 119-128.
  • [9] S. Noeiaghdam, D. Sidorov, and V. Sizikov, Control of accuracy on Taylor-collocation method to solve the weakly regular Volterra integral equations of the first kind by using the CESTAC method, Appl. Comput. Math., 19 (2020), 87-105.
  • [10] S. Noeiaghdam, D. Sidorov, A. M. Wazwaz, N. Sidorov, and V. Sizikov, The numerical validation of the Adomian decomposition method for solving Volterra integral equation with discontinuous kernels using the CESTAC method, Mathematics., 9 (2021), 260.
  • [11] D. Sidorov, Volterra integral equations of the first kind with jump discontinuous kernels, INV Follow-up Meeting Isaac Newton Institute for Mathematical Sciences (Feb 10-14, 2014, Cambridge, UK), 2014.
  • [12] D. N. Sidorov, Existence and blow-up of Kantorovich principal continuous solutions of nonlinear integral equations, Diff. Equat., 50 (2014), 1217–1224.
  • [13] D. Sidorov, Integral dynamical models: singularities, signals and control, In: L. O. Chua ed. World Scientific Series on Nonlinear Sciences Series A: Vol. 87, World Scientific Press, Singapore 2015.
  • [14] N. Sidorov, D. Sidorov, and A. Sinitsyn, Toward general theory of differential-operator and kinetic models, World Scientific Series on Nonlinear Science; Series A: Monographs and Treatises, 97; World Scientific Publishing Co. Pte. Ltd.: Hackensack, NJ, USA 2020.
  • [15] N. A. Sidorov and D. N. Sidorov, On the solvability of a class of Volterra operator equations of the first kind with piecewise continuous kernels, Math. Notes., 96 (2014), 811–826.
  • [16] D. N. Sidorov, On parametric families of solutions of Volterra integral equations of the first kind with piecewise smooth kernel, Differ. Equ., 49 (2013), 210–216.
  • [17] D. Sidorov, I. Muftahov, N. Tomin, D. Karamov, D. Panasetsky, A. Dreglea, F. Liu, and A. Foley, A dynamic analysis of energy storage with renewable and diesel generation using Volterra equations, IEEE Trans. Ind. Inform., 16 (2019), 3451-3459.
  • [18] D. Sidorov, Q. Tao, I. Muftahov, A. Zhukov, D. Karamov, A. Dreglea, and F. Liu, Energy balancing using charge/discharge storages control and load forecasts in a renewable-energy-based grids, Proc. of 38th China Control Conference (July 27-30, 2019, Guangzhou, China), IEEE., (2019), 1-6.
  • [19] D. Sidorov, A. Zhukov, A. Foley, A. Tynda, I. Muftahov, D. Panasetsky, and Y. Li, Volterra models in load leveling problem, E3S Web Conf., 69 (2018), 01015.
  • [20] A. Tynda, S. Noeiaghdam, and D. Sidorov, Polynomial spline collocation method for solving weakly regular Volterra integral equations of the first kind, The Bulletin of Irkutsk State University. Series Mathematics, 39 (2022), 62–79.
آمار
تعداد مشاهده مقاله: 534
تعداد دریافت فایل اصل مقاله: 1,055


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب