[1] Arino, O., Hbid, M.L., Dads, E. A., “Delay Differential Equations and Applications”, Springer, (2002).
[2] Bellen, A., Zennaro, M., “Numerical Methods for Delay Differential Equations”, Oxford: Oxford University Press, (2003).
[3] Driver, R. D., “Ordinary and Delay Differential Equation”, Springer, (1977).
[4] Yapman, Ö., Amiraliyev, G. M., Amirali, I., “Convergence Analysis of Fitted Numerical Method for a Singularly Perturbed Nonlinear Volterra Integro-Differential Equation with Delay”, Journal of Computational and Applied Mathematics, 355: 301-309, (2019).
[5] Dix, L. G., “Asymptotic Behavior of Solutions to a First-Order Differential Equation with Variable Delays”, Computers and Mathematics with Applications, 50: 1791-1800, (2005).
[6] Amirali, I., Cati, S., Amiraliyev, G. M., “Stability Inequalities for the Delay Pseudo-Parabolic Equations’’, International Journal of Applied Mathematics, 32(2): 289-294, (2019).
[7] Bellour, A., Bousselsal, M., “Numerical Solution of Delay Integro-Differential Equations by Using Taylor Collocation Method”, Mathematical Methods in Applied Science, 37: 1491-1506, (2013).
[8] Zhang, C., Niu, Y., “The Stability Relation Between Ordinary and Delay-Integro-Differential Equations”, Mathematical and Computer Modelling, Issues, 12, 49: 13-19, (2009).
[9] Kudu, M., Amirali, I., Amiraliyev, G. M., “A Finite Difference Method for a Singularly Perturbed Delay Integro-Differential Equation”, Journal of Computational and Applied Mathematics, 308: 379-390, (2016).
[10] Xiao-yong, Z., “A New Strategy for The Numerical Solution of Nonlinear Volterra Integral Equations with Vanishing Delays”, Applied Mathematics and Computation, 365: 124-608, (2020).
[11] Durmaz, M. E., Amiraliyev, G. M., “A Robust Numerical Method for a Singularly Perturbed Fredholm Integro-Differential Equation’’, Mediterranean Journal of Mathematics, 18(24): 1-17, (2021).
[12] Wu, S., Gan, S., “Analitical and Numerical Stability of Neutral Delay Integro-Differential Equations and Neutral Delay Partial Differential Equations”, Computers and Mathematics with Applications, 55: 2426-2443, (2008).
[13] Laib, H., Bellour, A., Bousselsal, M., “Numerical Solution of High-Order Linear Volterra Integro-Differential Equations by using Taylor Collocation Method’’, International Journal of Computer Mathematics, 96 (5): 1066-1085, (2019).
[14] Darania, P., Pishbin, S., “High-Order Collocation Methods for Nonlinear Delay Integral Equations”, Computational and Applied Mathematics, 326: 284-295, (2017).
[15] Panda, A, Mohapatra, J., Amirali, I., “A Second Order Post-Processing Technique for Singularly Perturbed Volterra Integro-Differential Equation”, Mediterranean Journal of Mathematics, 18(231): 1-25, (2021).
[16] Mohapatra, J., Natesan, S., “Uniform Convergence Analysis of finite Difference Scheme for Singularly Perturbed Delay Differential Equation on an Adaptively Generated Grid”, Numerical Mathematics: Theory, Methods and Applications, 3(1): 1-22, (2010).
[17] Amiraliyeva, I. G., Amiraliyev, G. M., “Uniform Difference Method For Parameterized Singularly Perturbed Delay Differential Equations”, Numerical Algorithms, 52(4): 509-521, (2009).
Stability Properties for the Delay Integro-Differential Equation
In this paper stability inequalities for the linear nonhomogeneous Volterra delay integro-differential equation (VDIDE) is being established. The particular problems are encountered to show the applicability of the method and to confirm the predicted theoretical analysis.
[1] Arino, O., Hbid, M.L., Dads, E. A., “Delay Differential Equations and Applications”, Springer, (2002).
[2] Bellen, A., Zennaro, M., “Numerical Methods for Delay Differential Equations”, Oxford: Oxford University Press, (2003).
[3] Driver, R. D., “Ordinary and Delay Differential Equation”, Springer, (1977).
[4] Yapman, Ö., Amiraliyev, G. M., Amirali, I., “Convergence Analysis of Fitted Numerical Method for a Singularly Perturbed Nonlinear Volterra Integro-Differential Equation with Delay”, Journal of Computational and Applied Mathematics, 355: 301-309, (2019).
[5] Dix, L. G., “Asymptotic Behavior of Solutions to a First-Order Differential Equation with Variable Delays”, Computers and Mathematics with Applications, 50: 1791-1800, (2005).
[6] Amirali, I., Cati, S., Amiraliyev, G. M., “Stability Inequalities for the Delay Pseudo-Parabolic Equations’’, International Journal of Applied Mathematics, 32(2): 289-294, (2019).
[7] Bellour, A., Bousselsal, M., “Numerical Solution of Delay Integro-Differential Equations by Using Taylor Collocation Method”, Mathematical Methods in Applied Science, 37: 1491-1506, (2013).
[8] Zhang, C., Niu, Y., “The Stability Relation Between Ordinary and Delay-Integro-Differential Equations”, Mathematical and Computer Modelling, Issues, 12, 49: 13-19, (2009).
[9] Kudu, M., Amirali, I., Amiraliyev, G. M., “A Finite Difference Method for a Singularly Perturbed Delay Integro-Differential Equation”, Journal of Computational and Applied Mathematics, 308: 379-390, (2016).
[10] Xiao-yong, Z., “A New Strategy for The Numerical Solution of Nonlinear Volterra Integral Equations with Vanishing Delays”, Applied Mathematics and Computation, 365: 124-608, (2020).
[11] Durmaz, M. E., Amiraliyev, G. M., “A Robust Numerical Method for a Singularly Perturbed Fredholm Integro-Differential Equation’’, Mediterranean Journal of Mathematics, 18(24): 1-17, (2021).
[12] Wu, S., Gan, S., “Analitical and Numerical Stability of Neutral Delay Integro-Differential Equations and Neutral Delay Partial Differential Equations”, Computers and Mathematics with Applications, 55: 2426-2443, (2008).
[13] Laib, H., Bellour, A., Bousselsal, M., “Numerical Solution of High-Order Linear Volterra Integro-Differential Equations by using Taylor Collocation Method’’, International Journal of Computer Mathematics, 96 (5): 1066-1085, (2019).
[14] Darania, P., Pishbin, S., “High-Order Collocation Methods for Nonlinear Delay Integral Equations”, Computational and Applied Mathematics, 326: 284-295, (2017).
[15] Panda, A, Mohapatra, J., Amirali, I., “A Second Order Post-Processing Technique for Singularly Perturbed Volterra Integro-Differential Equation”, Mediterranean Journal of Mathematics, 18(231): 1-25, (2021).
[16] Mohapatra, J., Natesan, S., “Uniform Convergence Analysis of finite Difference Scheme for Singularly Perturbed Delay Differential Equation on an Adaptively Generated Grid”, Numerical Mathematics: Theory, Methods and Applications, 3(1): 1-22, (2010).
[17] Amiraliyeva, I. G., Amiraliyev, G. M., “Uniform Difference Method For Parameterized Singularly Perturbed Delay Differential Equations”, Numerical Algorithms, 52(4): 509-521, (2009).
Amirali, İ. (2023). Stability Properties for the Delay Integro-Differential Equation. Gazi University Journal of Science, 36(2), 862-868. https://doi.org/10.35378/gujs.988728
AMA
Amirali İ. Stability Properties for the Delay Integro-Differential Equation. Gazi University Journal of Science. June 2023;36(2):862-868. doi:10.35378/gujs.988728
Chicago
Amirali, İlhame. “Stability Properties for the Delay Integro-Differential Equation”. Gazi University Journal of Science 36, no. 2 (June 2023): 862-68. https://doi.org/10.35378/gujs.988728.
EndNote
Amirali İ (June 1, 2023) Stability Properties for the Delay Integro-Differential Equation. Gazi University Journal of Science 36 2 862–868.
IEEE
İ. Amirali, “Stability Properties for the Delay Integro-Differential Equation”, Gazi University Journal of Science, vol. 36, no. 2, pp. 862–868, 2023, doi: 10.35378/gujs.988728.
ISNAD
Amirali, İlhame. “Stability Properties for the Delay Integro-Differential Equation”. Gazi University Journal of Science 36/2 (June 2023), 862-868. https://doi.org/10.35378/gujs.988728.
JAMA
Amirali İ. Stability Properties for the Delay Integro-Differential Equation. Gazi University Journal of Science. 2023;36:862–868.
MLA
Amirali, İlhame. “Stability Properties for the Delay Integro-Differential Equation”. Gazi University Journal of Science, vol. 36, no. 2, 2023, pp. 862-8, doi:10.35378/gujs.988728.
Vancouver
Amirali İ. Stability Properties for the Delay Integro-Differential Equation. Gazi University Journal of Science. 2023;36(2):862-8.