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

Year 2021, , 1263 - 1274, 31.12.2021
https://doi.org/10.16984/saufenbilder.668299

Abstract

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.

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References

  • [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.
Year 2021, , 1263 - 1274, 31.12.2021
https://doi.org/10.16984/saufenbilder.668299

Abstract

References

  • [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.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Falade Iyanda 0000-0001-7572-5688

Baoku Ismael 0000-0001-7572-5688

Tiamiyu Abdulgafar 0000-0001-7572-5688

Publication Date December 31, 2021
Submission Date December 31, 2019
Acceptance Date October 4, 2021
Published in Issue Year 2021

Cite

APA Iyanda, F., Ismael, B., & Abdulgafar, T. (2021). Numerical Assessment of Symmetric and Non-Symmetric Kernel Functions on Second Order Non-Homogenous Volterra Integro-Differential Equations. Sakarya University Journal of Science, 25(6), 1263-1274. https://doi.org/10.16984/saufenbilder.668299
AMA Iyanda F, Ismael B, Abdulgafar T. Numerical Assessment of Symmetric and Non-Symmetric Kernel Functions on Second Order Non-Homogenous Volterra Integro-Differential Equations. SAUJS. December 2021;25(6):1263-1274. doi:10.16984/saufenbilder.668299
Chicago Iyanda, Falade, Baoku Ismael, and Tiamiyu Abdulgafar. “Numerical Assessment of Symmetric and Non-Symmetric Kernel Functions on Second Order Non-Homogenous Volterra Integro-Differential Equations”. Sakarya University Journal of Science 25, no. 6 (December 2021): 1263-74. https://doi.org/10.16984/saufenbilder.668299.
EndNote Iyanda F, Ismael B, Abdulgafar T (December 1, 2021) Numerical Assessment of Symmetric and Non-Symmetric Kernel Functions on Second Order Non-Homogenous Volterra Integro-Differential Equations. Sakarya University Journal of Science 25 6 1263–1274.
IEEE F. Iyanda, B. Ismael, and T. Abdulgafar, “Numerical Assessment of Symmetric and Non-Symmetric Kernel Functions on Second Order Non-Homogenous Volterra Integro-Differential Equations”, SAUJS, vol. 25, no. 6, pp. 1263–1274, 2021, doi: 10.16984/saufenbilder.668299.
ISNAD Iyanda, Falade et al. “Numerical Assessment of Symmetric and Non-Symmetric Kernel Functions on Second Order Non-Homogenous Volterra Integro-Differential Equations”. Sakarya University Journal of Science 25/6 (December 2021), 1263-1274. https://doi.org/10.16984/saufenbilder.668299.
JAMA Iyanda F, Ismael B, Abdulgafar T. Numerical Assessment of Symmetric and Non-Symmetric Kernel Functions on Second Order Non-Homogenous Volterra Integro-Differential Equations. SAUJS. 2021;25:1263–1274.
MLA Iyanda, Falade et al. “Numerical Assessment of Symmetric and Non-Symmetric Kernel Functions on Second Order Non-Homogenous Volterra Integro-Differential Equations”. Sakarya University Journal of Science, vol. 25, no. 6, 2021, pp. 1263-74, doi:10.16984/saufenbilder.668299.
Vancouver Iyanda F, Ismael B, Abdulgafar T. Numerical Assessment of Symmetric and Non-Symmetric Kernel Functions on Second Order Non-Homogenous Volterra Integro-Differential Equations. SAUJS. 2021;25(6):1263-74.

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