Numerical Assessment of Symmetric and Non-Symmetric Kernel Functions on Second Order Non-Homogenous Volterra Integro-Differential Equations

Yıl 2021, Cilt: 25 Sayı: 6, 1263 - 1274, 31.12.2021

Falade Iyanda Baoku Ismael Tiamiyu Abdulgafar

https://doi.org/10.16984/saufenbilder.668299

Öz

In this paper, we present numerical assessment of symmetric and non-symmetric kernel functions on non-homogenous Volterra integro-differential equations. Simple MAPLE 18 software commands codes procedures are employ based on newly introduced techniques: exponentially fitted collocation approximation method and Adomian decomposition method for the numerical solutions of the non-homogenous Volterra integro-differential equations. The procedures are sought to obtain convergent point of the problems. Considering the property of symmetric and non-symmetric kernel ( Kt,s=Ks,t and Kt,s≠Ks,t ), the computational lengths are considered to archive the best numerical solutions for the four examples considered. The reliability and efficiency of the proposed techniques are demonstrated using some examples available in literature.

Anahtar Kelimeler

Symmetric and non-symmetric kernel functions, exponentially fitted collocation approximate method, non-homogenous Volterra integro-differential equations exponentially fitted collocation approximate method, Adomian decomposition method

Teşekkür

I shall be grateful,if my article is given positive and good attention

Kaynakça

• [1] P. Linz, “Analytic and Numerical Methods for Volterra Equations”, SIAM, Philadelphia, Pa, USA, Pp 132-139, 1985.
• [2] T. H. Christopher Baker, “Structure of recurrence relations in the study of stability in the numerical treatment of Volterra integral and integro-differential equation”, Journal of Integral Equations, 2 (1980) 11-29.
• [3] R. Kanwall, K. Liu. “A Taylor expansion approach for solving integral equations”. International Journal of Mathematical Education in Science and Technology, 20 (2006), 411–414, 1989.
• [4] S. Yuzbasi, N. Sahin, M. Sezer. “Bessel polynomial solutions of high-order linear Volterra integro-differential equations”. Computers & Mathematics with Applications, 62, 1940–1956, 2011.
• [5] Jalil Rashidinia and Ali Tahmasebi “Approximate solution of linear integro-differential equations by using modified Taylor expansion method” World Journal of Modelling and Simulation, 9(4), 300, 2013.
• [6] A. Avudainayagam, C. Vani, “Wavelet-Galerkin method for integro-differential equations”, Applied Numerical Mathematics, 32 (2000) 247-254.
• [7] J. Rashidinia, A. Tahmasebi, “Approximate solution of linear integro-differential equations by using modified Taylor expansion method”, World Journal of Modelling and Simulation, 9 (4) (2013), 289-301.
• [8] K. Maleknejad, F. Mirzaee and S. Abbasbandy, “Solving linear integro-differential equations system by using rationalized Haar functions method”, Applied Mathematical and Computation,155(2004), 317–328.
• [9] S.Q. Wang and J.H. He, “Variational iteration method for solving integro-differential equations”, Phys. Lett. A, 367 (2007), 188-191.
• [10] M. Mohseni Moghadam, H. Saeedi “Application of Differential Transforms for solving the Volterra Integro-Partial Differential Equations”, Iranian Journal of Science & Technology, Transaction A, Vol. 34, 2010.
• [11] J.H. He, “Homotopy perturbation technique”, Computation Meth. Appl. Mech. Eng., 178, 257-262 1999.
• [12] P. Linz, “Linear multi step methods for Volterra integro-differential equations”, Journal of the ACM (JACM), 16 (1969), 295-301.
• [13] Falade K.I “Solving Integro-Differential equations using exponentially fitted collocation approximate technique” Middle East Journal of Science 5(1) (2019), 73-85.
• [14] Abdul-Majid Wazwaz. “Linear and Nonlinear Integral Equations Methods and Applications” Saint Xavier University Chicago, IL 60655 April 20, 2011 pp 65-72.
• [15] Ramesh Kumar Vat, “M.SC. Mathematics MAL-644 Integral equation and symmetric kernel“ (2005) pp239-245.
• [16] G. Adomian, “Solving Frontier problems of physics: The decomposition method” Kluwer Pp 123-134, 1994.
• [17] K. Maleknejad and M. Hadizadeh, “A New computational method for Volterra-Fredholm integral equations”, Comput. Math. Appl., 37 (1999), 1–8.