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Year 2022, Volume: 51 Issue: 4, 995 - 1004, 01.08.2022
https://doi.org/10.15672/hujms.879507

Abstract

References

  • [1] N. Aronszajn, Theory of reproducing kernels, Cambridge, MA: Harvard University, 1951.
  • [2] A. Bellour and M. Bousselsal, Numerical solution of delay integro-differential equations by using Taylor collocation method, Math. Methods Appl. Sci. 37 (10), 1491- 1506, 2013.
  • [3] M. Cui and Z. Chen, The exact solution of nonlinear age-structured population model, Nonlinear Anal. Real World Appl. 8 (4), 1096-1112, 2007.
  • [4] M. Cui and F. Geng, A computational method for solving one-dimensional variable- coefficient Burgers equation, Appl. Math. Comput. 188 (2), 1389-1401, 2007.
  • [5] M. Cui and Y. Lin, Nonlinear numerical analysis in the reproducing Kernel space, New York: Nova Science, 2009.
  • [6] M. Cui, Y. Lin, and L. Yang, A new method of solving the coefficient inverse problem, Sci. China Math. 50 (4), 561-572, 2007.
  • [7] M. Fardi and M. Ghasemi, Solving nonlocal initial-boundary value problems for parabolic and hyperbolic integro-differential equations in reproducing kernel hilbert space, Numer Methods Partial Differ Equ. 33 (1), 174-198, 2016.
  • [8] M. Fardi, R.K. Ghaziani, and M. Ghasemi, The Reproducing Kernel Method for Some Variational Problems Depending on Indefinite Integrals, Math. Model. Anal. 21 (3), 412-429, 2016.
  • [9] F. Geng and M. Cui, Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space, Appl. Math. Comput. 192 (2), 389-398, 2007.
  • [10] F. Geng and M. Cui, Solving a nonlinear system of second order boundary value problems, J. Math. Anal. Appl. 327 (2), 1167-1181, 2007.
  • [11] M. Ghasemi, M. Fardi and R.K. Ghaziani, Numerical solution of nonlinear delay differential equations of fractional order in reproducing kernel Hilbert space, Appl. Math. Comput. 268, 815-831, 2015.
  • [12] V. Horvat, On polynomial spline collocation methods for neutral Volterra integro- differential equations with delay arguments, Proceedings of the 1. Conference on Ap- plied Mathematics and Computation, Dubrovnik, Croatia, 113-128, 1999.
  • [13] A. Makroglou, A block-by-block method for the numerical solution of Volterra delay integro-differential equations, Computing, 30 (1), 49-62, 1983.
  • [14] M. Mohammadi and R. Mokhtari, Solving the generalized regularized long wave equation on the basis of a reproducing kernel space, J. Comput. Appl. Math. 235 (14), 4003-4014, 2011.
  • [15] S. Vahdati, M. Fardi, and M. Ghasemi, Option pricing using a computational method based on reproducing kernel, J. Comput. Appl. Math. 328, 252-266, 2018.
  • [16] M. Xu and Y. Lin, Simplified reproducing kernel method for fractional differential equations with delay, Appl. Math. Lett. 52, 156-161, 2016.

A kernel-based method for Volterra delay integro-differential equations

Year 2022, Volume: 51 Issue: 4, 995 - 1004, 01.08.2022
https://doi.org/10.15672/hujms.879507

Abstract

Volterra integro-differential equations with constant delay $\tau>0$ are presented in this paper. We used a numerical method based on reproducing kernels to investigate well-known equations. The convergence analysis of the utilized approach is taken into account, which also provides the theoretical structure of the method. In addition, we derive some effective error estimates for the proposed method when applied to Volterra delay integro differential equations. Numerical experiments are carried out to illustrate the efficiency and applicability of the proposed method.

References

  • [1] N. Aronszajn, Theory of reproducing kernels, Cambridge, MA: Harvard University, 1951.
  • [2] A. Bellour and M. Bousselsal, Numerical solution of delay integro-differential equations by using Taylor collocation method, Math. Methods Appl. Sci. 37 (10), 1491- 1506, 2013.
  • [3] M. Cui and Z. Chen, The exact solution of nonlinear age-structured population model, Nonlinear Anal. Real World Appl. 8 (4), 1096-1112, 2007.
  • [4] M. Cui and F. Geng, A computational method for solving one-dimensional variable- coefficient Burgers equation, Appl. Math. Comput. 188 (2), 1389-1401, 2007.
  • [5] M. Cui and Y. Lin, Nonlinear numerical analysis in the reproducing Kernel space, New York: Nova Science, 2009.
  • [6] M. Cui, Y. Lin, and L. Yang, A new method of solving the coefficient inverse problem, Sci. China Math. 50 (4), 561-572, 2007.
  • [7] M. Fardi and M. Ghasemi, Solving nonlocal initial-boundary value problems for parabolic and hyperbolic integro-differential equations in reproducing kernel hilbert space, Numer Methods Partial Differ Equ. 33 (1), 174-198, 2016.
  • [8] M. Fardi, R.K. Ghaziani, and M. Ghasemi, The Reproducing Kernel Method for Some Variational Problems Depending on Indefinite Integrals, Math. Model. Anal. 21 (3), 412-429, 2016.
  • [9] F. Geng and M. Cui, Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space, Appl. Math. Comput. 192 (2), 389-398, 2007.
  • [10] F. Geng and M. Cui, Solving a nonlinear system of second order boundary value problems, J. Math. Anal. Appl. 327 (2), 1167-1181, 2007.
  • [11] M. Ghasemi, M. Fardi and R.K. Ghaziani, Numerical solution of nonlinear delay differential equations of fractional order in reproducing kernel Hilbert space, Appl. Math. Comput. 268, 815-831, 2015.
  • [12] V. Horvat, On polynomial spline collocation methods for neutral Volterra integro- differential equations with delay arguments, Proceedings of the 1. Conference on Ap- plied Mathematics and Computation, Dubrovnik, Croatia, 113-128, 1999.
  • [13] A. Makroglou, A block-by-block method for the numerical solution of Volterra delay integro-differential equations, Computing, 30 (1), 49-62, 1983.
  • [14] M. Mohammadi and R. Mokhtari, Solving the generalized regularized long wave equation on the basis of a reproducing kernel space, J. Comput. Appl. Math. 235 (14), 4003-4014, 2011.
  • [15] S. Vahdati, M. Fardi, and M. Ghasemi, Option pricing using a computational method based on reproducing kernel, J. Comput. Appl. Math. 328, 252-266, 2018.
  • [16] M. Xu and Y. Lin, Simplified reproducing kernel method for fractional differential equations with delay, Appl. Math. Lett. 52, 156-161, 2016.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Mojtaba Fardi This is me 0000-0002-7741-5322

Yasir Khan 0000-0002-6386-6181

Ebrahim Amını This is me 0000-0001-7100-1199

Publication Date August 1, 2022
Published in Issue Year 2022 Volume: 51 Issue: 4

Cite

APA Fardi, M., Khan, Y., & Amını, E. (2022). A kernel-based method for Volterra delay integro-differential equations. Hacettepe Journal of Mathematics and Statistics, 51(4), 995-1004. https://doi.org/10.15672/hujms.879507
AMA Fardi M, Khan Y, Amını E. A kernel-based method for Volterra delay integro-differential equations. Hacettepe Journal of Mathematics and Statistics. August 2022;51(4):995-1004. doi:10.15672/hujms.879507
Chicago Fardi, Mojtaba, Yasir Khan, and Ebrahim Amını. “A Kernel-Based Method for Volterra Delay Integro-Differential Equations”. Hacettepe Journal of Mathematics and Statistics 51, no. 4 (August 2022): 995-1004. https://doi.org/10.15672/hujms.879507.
EndNote Fardi M, Khan Y, Amını E (August 1, 2022) A kernel-based method for Volterra delay integro-differential equations. Hacettepe Journal of Mathematics and Statistics 51 4 995–1004.
IEEE M. Fardi, Y. Khan, and E. Amını, “A kernel-based method for Volterra delay integro-differential equations”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 4, pp. 995–1004, 2022, doi: 10.15672/hujms.879507.
ISNAD Fardi, Mojtaba et al. “A Kernel-Based Method for Volterra Delay Integro-Differential Equations”. Hacettepe Journal of Mathematics and Statistics 51/4 (August 2022), 995-1004. https://doi.org/10.15672/hujms.879507.
JAMA Fardi M, Khan Y, Amını E. A kernel-based method for Volterra delay integro-differential equations. Hacettepe Journal of Mathematics and Statistics. 2022;51:995–1004.
MLA Fardi, Mojtaba et al. “A Kernel-Based Method for Volterra Delay Integro-Differential Equations”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 4, 2022, pp. 995-1004, doi:10.15672/hujms.879507.
Vancouver Fardi M, Khan Y, Amını E. A kernel-based method for Volterra delay integro-differential equations. Hacettepe Journal of Mathematics and Statistics. 2022;51(4):995-1004.