The study establishes the stability bounds of the second-order neutral Volterra integro-differential equation concerning both the right-side and initial conditions. The examples are given to show the applicability of the method and confirm the predicted theoretical analysis.
Darania, P., Ebadian, A., A method for the numerical solution of the integro-differential equations, Appl. Math. Comput., 188(1) (2007), 657–668. https://doi.org/10.1016/j.amc.2006.10.046
Bahuguna, D., Ujlayan, A., Pandey, D. N., A comparative study of numerical methods for solving an integro-differential equation, Comput. Math. Appl., 57(9) (2009), 1485–1493. https://doi.org/10.1016/j.camwa.2008.10.097
Shahmorad, S., Ostadzad, M. H., Baleanu, D., A tau–like numerical method for solving fractional delay integro–differential equations, Appl. Numer. Math., 151 (2020), 322–336. https://doi.org/10.1016/j.apnum.2020.01.006
Hamoud, A. A., Mohammed, N. M., Ghadle, K. P., Dhondge, S. L., Solving integro-differential equations by using numerical techniques, Int. J. Appl. Eng. Res., 14(14) (2019), 3219–3225.
Ozkan, O., Numerical implementation of differential transformations method for integro-differential equations, Int. J. Comput. Math., 87(12) (2010), 2786–2797. https://doi.org/10.1080/00207160902795627
Boykov, I. V., Roudnev, V. A., Boykova, A. I., Stability of solutions of systems of Volterra integral equations, Appl. Math. Comput., 475 (2024), 128728. https://doi.org/10.1016/j.amc.2024.128728
Ngoc, P. H. A., Anh, T. T., New stability criteria for nonlinear Volterra integro-differential equations, Acta Math. Vietnam., 43 (2018), 485–501. https://doi.org/10.1007/s40306-017-0243-y
Amirali, I., Stability properties for the delay integro-differential equation, GAU J. Sci., 36(2) (2023), 862-868. 10.35378/gujs.988728
Alahmadi, F., Raffoul, Y. N., Alharbi, S., Boundedness and stability of solutions of nonlinear Volterra integro-differential equations, Adv. Dyn. Syst. Appl., 13(1) (2018), 19–31.
Zhao, J. J., Xu, Y., Liu, M. Z., Stability analysis of numerical methods for linear neutral Volterra delay integro-differential system, Appl. Math. Comput., 167(2) (2005), 1062–1079. https://doi.org/10.1016/j.amc.2004.08.003
Amirali, I., Acar, H., Stability inequalities and numerical solution for neutral Volterra delay integro-differential equation, J. Comput. Appl. Math., 436 (2024), 115343. https://doi.org/10.1016/j.cam.2023.115343
Murakami, S., Ngoc, P., On stability and robust stability of positive linear Volterra equations in Banach lattices, Open Math., 8(5) (2010), 966–984. https://doi.org/10.2478/s11533-010-0061-0
Amirali, I., Acar, H., A novel approach for the stability inequalities for high-order Volterra delay integro-differential equation, J. Appl. Math. Comput., 69(1) (2023), 1057–1069. https://doi.org/10.1007/s12190-022-01761-8
Yapman, O., Amiraliyev, G. M., Amirali, I., Convergence analysis of fitted numerical method for a singularly perturbed nonlinear Volterra integro-differential equation with delay, J. Comput. Appl. Math., 355 (2019), 301–309. https://doi.org/10.1016/j.cam.2019.01.026
Amirali, I., Fedakar, B., Amiraliyev, G. M., On the second-order neutral Volterra integro-differential equation and its numerical solution, Appl. Math. Comput., 476 (2024), 128765. https://doi.org/10.1016/j.amc.2024.128765
Panda, A., Mohapatra, J., Amirali, I., A second-order post-processing technique for singularly perturbed Volterra integro-differential equations, Mediterr. J. Math., 18 (2021), 231.
https://doi.org/10.1007/s00009-021-01873-8
Darania, P., Ebadian, A., A method for the numerical solution of the integro-differential equations, Appl. Math. Comput., 188(1) (2007), 657–668. https://doi.org/10.1016/j.amc.2006.10.046
Bahuguna, D., Ujlayan, A., Pandey, D. N., A comparative study of numerical methods for solving an integro-differential equation, Comput. Math. Appl., 57(9) (2009), 1485–1493. https://doi.org/10.1016/j.camwa.2008.10.097
Shahmorad, S., Ostadzad, M. H., Baleanu, D., A tau–like numerical method for solving fractional delay integro–differential equations, Appl. Numer. Math., 151 (2020), 322–336. https://doi.org/10.1016/j.apnum.2020.01.006
Hamoud, A. A., Mohammed, N. M., Ghadle, K. P., Dhondge, S. L., Solving integro-differential equations by using numerical techniques, Int. J. Appl. Eng. Res., 14(14) (2019), 3219–3225.
Ozkan, O., Numerical implementation of differential transformations method for integro-differential equations, Int. J. Comput. Math., 87(12) (2010), 2786–2797. https://doi.org/10.1080/00207160902795627
Boykov, I. V., Roudnev, V. A., Boykova, A. I., Stability of solutions of systems of Volterra integral equations, Appl. Math. Comput., 475 (2024), 128728. https://doi.org/10.1016/j.amc.2024.128728
Ngoc, P. H. A., Anh, T. T., New stability criteria for nonlinear Volterra integro-differential equations, Acta Math. Vietnam., 43 (2018), 485–501. https://doi.org/10.1007/s40306-017-0243-y
Amirali, I., Stability properties for the delay integro-differential equation, GAU J. Sci., 36(2) (2023), 862-868. 10.35378/gujs.988728
Alahmadi, F., Raffoul, Y. N., Alharbi, S., Boundedness and stability of solutions of nonlinear Volterra integro-differential equations, Adv. Dyn. Syst. Appl., 13(1) (2018), 19–31.
Zhao, J. J., Xu, Y., Liu, M. Z., Stability analysis of numerical methods for linear neutral Volterra delay integro-differential system, Appl. Math. Comput., 167(2) (2005), 1062–1079. https://doi.org/10.1016/j.amc.2004.08.003
Amirali, I., Acar, H., Stability inequalities and numerical solution for neutral Volterra delay integro-differential equation, J. Comput. Appl. Math., 436 (2024), 115343. https://doi.org/10.1016/j.cam.2023.115343
Murakami, S., Ngoc, P., On stability and robust stability of positive linear Volterra equations in Banach lattices, Open Math., 8(5) (2010), 966–984. https://doi.org/10.2478/s11533-010-0061-0
Amirali, I., Acar, H., A novel approach for the stability inequalities for high-order Volterra delay integro-differential equation, J. Appl. Math. Comput., 69(1) (2023), 1057–1069. https://doi.org/10.1007/s12190-022-01761-8
Yapman, O., Amiraliyev, G. M., Amirali, I., Convergence analysis of fitted numerical method for a singularly perturbed nonlinear Volterra integro-differential equation with delay, J. Comput. Appl. Math., 355 (2019), 301–309. https://doi.org/10.1016/j.cam.2019.01.026
Amirali, I., Fedakar, B., Amiraliyev, G. M., On the second-order neutral Volterra integro-differential equation and its numerical solution, Appl. Math. Comput., 476 (2024), 128765. https://doi.org/10.1016/j.amc.2024.128765
Panda, A., Mohapatra, J., Amirali, I., A second-order post-processing technique for singularly perturbed Volterra integro-differential equations, Mediterr. J. Math., 18 (2021), 231.
https://doi.org/10.1007/s00009-021-01873-8
There are 17 citations in total.
Details
Primary Language
English
Subjects
Numerical Analysis, Ordinary Differential Equations, Difference Equations and Dynamical Systems
Fedakar, B., & Amirali, İ. (n.d.). Stability analysis of neutral Volterra integro-differential equation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 73(4), 1088-1097. https://doi.org/10.31801/cfsuasmas.1360251
Fedakar, Burcu, and İlhame Amirali. “Stability Analysis of Neutral Volterra Integro-Differential Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73, no. 4 n.d.: 1088-97. https://doi.org/10.31801/cfsuasmas.1360251.
EndNote
Fedakar B, Amirali İ Stability analysis of neutral Volterra integro-differential equation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73 4 1088–1097.
IEEE
B. Fedakar and İ. Amirali, “Stability analysis of neutral Volterra integro-differential equation”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 73, no. 4, pp. 1088–1097, doi: 10.31801/cfsuasmas.1360251.
ISNAD
Fedakar, Burcu - Amirali, İlhame. “Stability Analysis of Neutral Volterra Integro-Differential Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73/4 (n.d.), 1088-1097. https://doi.org/10.31801/cfsuasmas.1360251.
JAMA
Fedakar B, Amirali İ. Stability analysis of neutral Volterra integro-differential equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.;73:1088–1097.
MLA
Fedakar, Burcu and İlhame Amirali. “Stability Analysis of Neutral Volterra Integro-Differential Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 73, no. 4, pp. 1088-97, doi:10.31801/cfsuasmas.1360251.