Research Article
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Year 2022, Volume: 71 Issue: 4, 954 - 967, 30.12.2022

Muhammet Enes Durmaz Musa Çakır Gabil Amirali

https://doi.org/10.31801/cfsuasmas.1072728
Cited By: 4

Abstract

References

  • Amiraliyev, G. M., Durmaz, M. E., Kudu, M., Uniform convergence results for singularly perturbed Fredholm integro-differential equation, J. Math. Anal., 9(6) (2018), 55–64.
  • Amiraliyev, G. M., Durmaz, M. E., Kudu, M., Fitted second order numerical method for a singularly perturbed Fredholm integro-differential equation, Bull. Belg. Math. Soc. Simon Steven., 27(1) (2020), 71–88. https://doi.org/10.36045/bbms/1590199305
  • Amiraliyev, G. M., Durmaz, M. E., Kudu, M., A numerical method for a second order singularly perturbed Fredholm integro-differential equation, Miskolc Math. Notes., 22(1) (2021), 37–48. https://doi.org/10.18514/MMN.2021.2930
  • Amiraliyev, G. M., Mamedov, Y. D., Difference schemes on the uniform mesh for singularly perturbed pseudo-parabolic equations, Turk. J. Math., 19 (1995), 207–222.
  • Brunner, H., Numerical Analysis and Computational Solution of Integro-Differential Equations, Contemporary Computational Mathematics-A Celebration of the 80th Birthday of Ian Sloan (J. Dick et al., eds.), Springer, Cham, 2018, 205–231. https://doi.org 10.1007/978-3-319-72456-0 11
  • Chen, J., He, M., Zeng, T., A multiscale Galerkin method for second-order boundary value problems of Fredholm integro differential equation II: Efficient algorithm for the discrete linear system, J. Vis. Commun. Image R., 58 (2019), 112–118. https://doi.org/10.1016/j.jvcir.2018.11.027
  • Chen, J., He, M., Huang, Y., A fast multiscale Galerkin method for solving second order linear Fredholm integro-differential equation with Dirichlet boundary conditions, J. Comput. Appl. Math., 364 (2020), 112352. https://doi.org/10.1016/j.cam.2019.112352
  • Dehghan, M., Chebyshev finite difference for Fredholm integro-differential equation, Int. J. Comput. Math., 85 (1) (2008), 123–130. https://doi.org/10.1080/00207160701405436
  • Doolan, E. R., Miller, J. J. H., Schilders, W. H. A., Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole Press, Dublin, 1980.
  • Durmaz, M. E., Amiraliyev, G. M., A robust numerical method for a singularly perturbed Fredholm integro-differential equation, Mediterr. J. Math., 18(24) (2021), 1–17. https://doi.org/10.1007/s00009-020-01693-2
  • Durmaz, M. E., Amiraliyev, G. M., Kudu, M., Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition, Turk. J. Math., 46(1) (2022), 207–224. https://doi.org/10.3906/mat-2109-11
  • Farrell, P. A., Hegarty, A. F., Miller, J. J. H., O’Riordan, E., Shishkin, G. I., Robust Computational Techniques for Boundary Layers, Chapman Hall/CRC, New York, 2000. https://doi.org/10.1201/9781482285727
  • Jalilian, R., Tahernezhad, T., Exponential spline method for approximation solution of Fredholm integro-differential equation, Int. J. Comput. Math., 97(4) (2020), 791–801. https://doi.org/10.1080/00207160.2019.1586891
  • Jalius, C., Majid, Z. A., Numerical solution of second-order Fredholm integro differential equations with boundary conditions by quadrature-difference method, J. Appl. Math., (2017). https://doi.org/10.1155/2017/2645097
  • Kadalbajoo, M. K., Gupta, V., A brief survey on numerical methods for solving singularly perturbed problems, Appl. Math. Comput., 217 (2010), 3641–3716. https://doi.org/10.1016/j.amc.2010.09.059
  • Karim, M. F., Mohamad, M., Rusiman, M. S., Che-him, N., Roslan, R., Khalid, K., ADM for solving linear second-order Fredholm integro-differential equations, Journal of Physics, (2018), 995. https://doi.org/10.1088/1742-6596/995/1/012009
  • Kudu, M., Amirali, I., Amiraliyev, G. M., A finite-difference method for a singularly perturbed delay integro-differential equation, J. Comput. Appl. Math., 308 (2016), 379–390. https://doi.org/10.1016/j.cam.2016.06.018
  • Miller, J. J. H., O’Riordan, E., Shishkin, G. I., Fitted Numerical Methods for Singular Perturbation Problems, World Scientific, Singapore, 1996.
  • Nayfeh, A. H., Introduction to Perturbation Techniques, Wiley, New York, 1993.
  • O’Malley, R. E., Singular Perturbations Methods for Ordinary Differential Equations, Springer, New York, 1991. https://doi.org/10.1007/978-1-4612-0977-5
  • Roos, H. G., Stynes, M., Tobiska, L., Numerical Methods for Singularly Perturbed Differential Equations, Springer-Verlaq, Berlin, 1996. https://doi.org/10.1007/978-3-662-03206-0
  • Samarskii, A. A., The Theory of Difference Schemes(1st ed.), CRC Press, 2001. https://doi.org/10.1201/9780203908518
  • Shahsavaran, A., On the convergence of Lagrange interpolation to solve special type of second kind Fredholm integro differential equations, Appl. Math. Sci., 6(7) (2012), 343–348.
  • Yapman, Ö., 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), 301309. https://doi.org/10.1016/j.cam.2019.01.026
  • Yapman, Ö., Amiraliyev, G. M., A novel second–order fitted computational method for a singularly perturbed Volterra integro-differential equation, Int. J. Comput. Math., 97(6) (2020), 1293–1302. https://doi.org/10.1080/00207160.2019.1614565
  • Xue, Q., Niu, J., Yu, D., Ran, C., An improved reproducing kernel method for Fredholm integro-differential type two-point boundary value problems, Int. J. Comput. Math., 95(5) (2018), 1015–1023. https://doi.org/10.1080/00207160.2017.1322201

Parameter uniform second-order numerical approximation for the integro-differential equations involving boundary layers

Year 2022, Volume: 71 Issue: 4, 954 - 967, 30.12.2022

Muhammet Enes Durmaz Musa Çakır Gabil Amirali

https://doi.org/10.31801/cfsuasmas.1072728
Cited By: 4

Abstract

The work handles a Fredholm integro-differential equation involving boundary layers. A fitted second-order difference scheme has been created on a uniform mesh utilizing interpolating quadrature rules and exponential basis functions. The stability and convergence of the proposed discretization technique are analyzed and one example is solved to display the advantages of the presented technique.

Keywords

Finite difference method Fredholm integro-differential equation singular perturbation uniform convergence

References

  • Amiraliyev, G. M., Durmaz, M. E., Kudu, M., Uniform convergence results for singularly perturbed Fredholm integro-differential equation, J. Math. Anal., 9(6) (2018), 55–64.
  • Amiraliyev, G. M., Durmaz, M. E., Kudu, M., Fitted second order numerical method for a singularly perturbed Fredholm integro-differential equation, Bull. Belg. Math. Soc. Simon Steven., 27(1) (2020), 71–88. https://doi.org/10.36045/bbms/1590199305
  • Amiraliyev, G. M., Durmaz, M. E., Kudu, M., A numerical method for a second order singularly perturbed Fredholm integro-differential equation, Miskolc Math. Notes., 22(1) (2021), 37–48. https://doi.org/10.18514/MMN.2021.2930
  • Amiraliyev, G. M., Mamedov, Y. D., Difference schemes on the uniform mesh for singularly perturbed pseudo-parabolic equations, Turk. J. Math., 19 (1995), 207–222.
  • Brunner, H., Numerical Analysis and Computational Solution of Integro-Differential Equations, Contemporary Computational Mathematics-A Celebration of the 80th Birthday of Ian Sloan (J. Dick et al., eds.), Springer, Cham, 2018, 205–231. https://doi.org 10.1007/978-3-319-72456-0 11
  • Chen, J., He, M., Zeng, T., A multiscale Galerkin method for second-order boundary value problems of Fredholm integro differential equation II: Efficient algorithm for the discrete linear system, J. Vis. Commun. Image R., 58 (2019), 112–118. https://doi.org/10.1016/j.jvcir.2018.11.027
  • Chen, J., He, M., Huang, Y., A fast multiscale Galerkin method for solving second order linear Fredholm integro-differential equation with Dirichlet boundary conditions, J. Comput. Appl. Math., 364 (2020), 112352. https://doi.org/10.1016/j.cam.2019.112352
  • Dehghan, M., Chebyshev finite difference for Fredholm integro-differential equation, Int. J. Comput. Math., 85 (1) (2008), 123–130. https://doi.org/10.1080/00207160701405436
  • Doolan, E. R., Miller, J. J. H., Schilders, W. H. A., Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole Press, Dublin, 1980.
  • Durmaz, M. E., Amiraliyev, G. M., A robust numerical method for a singularly perturbed Fredholm integro-differential equation, Mediterr. J. Math., 18(24) (2021), 1–17. https://doi.org/10.1007/s00009-020-01693-2
  • Durmaz, M. E., Amiraliyev, G. M., Kudu, M., Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition, Turk. J. Math., 46(1) (2022), 207–224. https://doi.org/10.3906/mat-2109-11
  • Farrell, P. A., Hegarty, A. F., Miller, J. J. H., O’Riordan, E., Shishkin, G. I., Robust Computational Techniques for Boundary Layers, Chapman Hall/CRC, New York, 2000. https://doi.org/10.1201/9781482285727
  • Jalilian, R., Tahernezhad, T., Exponential spline method for approximation solution of Fredholm integro-differential equation, Int. J. Comput. Math., 97(4) (2020), 791–801. https://doi.org/10.1080/00207160.2019.1586891
  • Jalius, C., Majid, Z. A., Numerical solution of second-order Fredholm integro differential equations with boundary conditions by quadrature-difference method, J. Appl. Math., (2017). https://doi.org/10.1155/2017/2645097
  • Kadalbajoo, M. K., Gupta, V., A brief survey on numerical methods for solving singularly perturbed problems, Appl. Math. Comput., 217 (2010), 3641–3716. https://doi.org/10.1016/j.amc.2010.09.059
  • Karim, M. F., Mohamad, M., Rusiman, M. S., Che-him, N., Roslan, R., Khalid, K., ADM for solving linear second-order Fredholm integro-differential equations, Journal of Physics, (2018), 995. https://doi.org/10.1088/1742-6596/995/1/012009
  • Kudu, M., Amirali, I., Amiraliyev, G. M., A finite-difference method for a singularly perturbed delay integro-differential equation, J. Comput. Appl. Math., 308 (2016), 379–390. https://doi.org/10.1016/j.cam.2016.06.018
  • Miller, J. J. H., O’Riordan, E., Shishkin, G. I., Fitted Numerical Methods for Singular Perturbation Problems, World Scientific, Singapore, 1996.
  • Nayfeh, A. H., Introduction to Perturbation Techniques, Wiley, New York, 1993.
  • O’Malley, R. E., Singular Perturbations Methods for Ordinary Differential Equations, Springer, New York, 1991. https://doi.org/10.1007/978-1-4612-0977-5
  • Roos, H. G., Stynes, M., Tobiska, L., Numerical Methods for Singularly Perturbed Differential Equations, Springer-Verlaq, Berlin, 1996. https://doi.org/10.1007/978-3-662-03206-0
  • Samarskii, A. A., The Theory of Difference Schemes(1st ed.), CRC Press, 2001. https://doi.org/10.1201/9780203908518
  • Shahsavaran, A., On the convergence of Lagrange interpolation to solve special type of second kind Fredholm integro differential equations, Appl. Math. Sci., 6(7) (2012), 343–348.
  • Yapman, Ö., 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), 301309. https://doi.org/10.1016/j.cam.2019.01.026
  • Yapman, Ö., Amiraliyev, G. M., A novel second–order fitted computational method for a singularly perturbed Volterra integro-differential equation, Int. J. Comput. Math., 97(6) (2020), 1293–1302. https://doi.org/10.1080/00207160.2019.1614565
  • Xue, Q., Niu, J., Yu, D., Ran, C., An improved reproducing kernel method for Fredholm integro-differential type two-point boundary value problems, Int. J. Comput. Math., 95(5) (2018), 1015–1023. https://doi.org/10.1080/00207160.2017.1322201
There are 26 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Articles
Authors

Muhammet Enes Durmaz 0000-0002-6216-1032

Musa Çakır 0000-0002-1979-570X

Gabil Amirali 0000-0001-6585-7353

Publication Date December 30, 2022
Submission Date February 13, 2022
Acceptance Date May 5, 2022
Published in Issue Year 2022 Volume: 71 Issue: 4

Cite

APA Durmaz, M. E., Çakır, M., & Amirali, G. (2022). Parameter uniform second-order numerical approximation for the integro-differential equations involving boundary layers. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(4), 954-967. https://doi.org/10.31801/cfsuasmas.1072728
AMA Durmaz ME, Çakır M, Amirali G. Parameter uniform second-order numerical approximation for the integro-differential equations involving boundary layers. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2022;71(4):954-967. doi:10.31801/cfsuasmas.1072728
Chicago Durmaz, Muhammet Enes, Musa Çakır, and Gabil Amirali. “Parameter Uniform Second-Order Numerical Approximation for the Integro-Differential Equations Involving Boundary Layers”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, no. 4 (December 2022): 954-67. https://doi.org/10.31801/cfsuasmas.1072728.
EndNote Durmaz ME, Çakır M, Amirali G (December 1, 2022) Parameter uniform second-order numerical approximation for the integro-differential equations involving boundary layers. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 4 954–967.
IEEE M. E. Durmaz, M. Çakır, and G. Amirali, “Parameter uniform second-order numerical approximation for the integro-differential equations involving boundary layers”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 71, no. 4, pp. 954–967, 2022, doi: 10.31801/cfsuasmas.1072728.
ISNAD Durmaz, Muhammet Enes et al. “Parameter Uniform Second-Order Numerical Approximation for the Integro-Differential Equations Involving Boundary Layers”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/4 (December 2022), 954-967. https://doi.org/10.31801/cfsuasmas.1072728.
JAMA Durmaz ME, Çakır M, Amirali G. Parameter uniform second-order numerical approximation for the integro-differential equations involving boundary layers. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:954–967.
MLA Durmaz, Muhammet Enes et al. “Parameter Uniform Second-Order Numerical Approximation for the Integro-Differential Equations Involving Boundary Layers”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 71, no. 4, 2022, pp. 954-67, doi:10.31801/cfsuasmas.1072728.
Vancouver Durmaz ME, Çakır M, Amirali G. Parameter uniform second-order numerical approximation for the integro-differential equations involving boundary layers. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(4):954-67.

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