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Applied & Interdisciplinary Mathematics

Singularly perturbed reaction diffusion problem with large spatial delay via non-standard fitted operator method

ORCID Icon, ORCID Icon & ORCID Icon | (Reviewing editor:)
Article: 2171698 | Received 09 Sep 2022, Accepted 19 Jan 2023, Published online: 02 Mar 2023

References

  • Ayele, M. A., Tiruneh, A. A., & Derese, G. A. (2022). Fitted scheme for singularly perturbed time delay reaction-diffusion problems. Iranian Journal of Numerical Analysis and Optimization. https://doi.org/10.22067/ijnao.2022.77453.1161
  • Ayele, M. A., Tiruneh, A. A., Derese, G. A., & Araci, S. (2022). Uniformly convergent scheme for singularly perturbed space delay parabolic differential equation with discontinuous convection coefficient and source term. Journal of Mathematics, 2022, 1–15. https://doi.org/10.1155/2022/1874741
  • Babu, G., & Bansal, K. (2022). A high order robust numerical scheme for singularly perturbed delay parabolic convection diffusion problems. Journal of Applied Mathematics and Computing, 68(1), 363–389. https://doi.org/10.1007/s12190-021-01512-1
  • Bansal, K., Rai, P., & Sharma, K. K. (2017). Numerical treatment for the class of time dependent singularly perturbed parabolic problems with general shift arguments. Differential Equations and Dynamical Systems, 25(2), 327–346. https://doi.org/10.1007/s12591-015-0265-7
  • Bansal, K., & Sharma, K. K. (2017). Parameter uniform numerical scheme for time dependent singularly perturbed convection-diffusion-reaction problems with general shift arguments. Numerical Algorithms, 75(1), 113–145. https://doi.org/10.1007/s11075-016-0199-3
  • Bansal, K., & Sharma, K. K. (2018). Parameter-robust numerical scheme for time-dependent singularly perturbed reaction–diffusion problem with large delay. Numerical Functional Analysis and Optimization, 39(2), 127–154. https://doi.org/10.1080/01630563.2016.1277742
  • Brdar, M., Franz, S., Ludwig, L., & Roos, H. G. (2023). A balanced norm error estimation for the time-dependent reaction-diffusion problem with shift in space. Applied Mathematics and Computation, 437, 127507. https://doi.org/10.1016/j.amc.2022.127507
  • Burcu, G. (2021). A computational technique for solving singularly perturbed delay partial differential equations. Foundations of Computing and Decision Sciences, 46(3), 221–233. https://doi.org/10.2478/fcds-2021-0015
  • Choudhary, M., & Kaushik, A. (2022). A uniformly convergent defect correction method for parabolic singular perturbation problems with a large delay. Journal of Applied Mathematics and Computing, 1–25. https://doi.org/10.1007/s12190-022-01796-x
  • Clavero, C., & Gracia, J. L. (2010). On the uniform convergence of a finite difference scheme for time dependent singularly perturbed reaction-diffusion problems. Applied Mathematics and Computation, 216(5), 1478–1488. https://doi.org/10.1016/j.amc.2010.02.050
  • Daba, I. T., & Duressa, G. F. (2021). Hybrid algorithm for singularly perturbed delay parabolic partial differential equations. Applications and Applied Mathematics: An International Journal (AAM), 16(1), 21. https://digitalcommons.pvamu.edu/aam/vol16/iss1/21
  • Duressa, G. F., & Woldaregay, M. M. (2022). Fitted numerical scheme for solving singularly perturbed parabolic delay partial differential equations. Tamkang Journal of Mathematics, 53. https://doi.org/10.5556/j.tkjm.53.2022.3638
  • Ejere, A. H., Duressa, G. F., Woldaregay, M. M., & Dinka, T. G. (2022). A uniformly convergent numerical scheme for solving singularly perturbed differential equations with large spatial delay. SN Applied Sciences, 4(12), 1–15. https://doi.org/10.1007/s42452-022-05203-9
  • Elango, S., Tamilselvan, A., Vadivel, R., Gunasekaran, N., Zhu, H., Cao, J., & Xiaodi, L. (2021). Finite difference scheme for singularly perturbed reaction diffusion problem of partial delay differential equation with nonlocal boundary condition. Advances in Difference Equations, 2021(1), 1–20. https://doi.org/10.1186/s13662-021-03296-x
  • Gelu, F. W., Duressa, G. F., & Kovtunenko, V. (2021). A uniformly convergent collocation method for singularly perturbed delay parabolic reaction-diffusion problem.abstract and Applied Analysis, 2021, 1–11. Hindawi. https://doi.org/10.1155/2021/8835595
  • Gobena, W. T., Duressa, G. F., & Scapellato, A. (2021). Parameter-uniform numerical scheme for singularly perturbed delay parabolic reaction diffusion equations with integral boundary condition. International Journal of Differential Equations, 2021, 1–16. https://doi.org/10.1155/2021/9993644
  • Govindarao, L., Mohapatra, J., & Das, A. (2020). A fourth-order numerical scheme for singularly perturbed delay parabolic problem arising in population dynamics. Journal of Applied Mathematics and Computing, 63(1), 171–195. https://doi.org/10.1007/s12190-019-01313-7
  • Hailu, W. S., Duressa, G. F., & Liu, L. (2022). Parameter- uniform cubic spline method for singularly perturbed parabolic differential equation with large negative shift and integral boundary condition. Research in Mathematics, 9(1), 2151080. https://doi.org/10.1080/27684830.2022.2151080
  • Kaushik, A., & Sharma, N. (2020). An adaptive difference scheme for parabolic delay differential equation with discontinuous coefficients and interior layers. Journal of Difference Equations and Applications, 26(11–12), 1450–1470. https://doi.org/10.1080/10236198.2020.1843645
  • Kumar, D. (2021). A parameter-uniform scheme for the parabolic singularly perturbed problem with a delay in time. Numerical Methods for Partial Differential Equations, 37(1), 626–642. https://doi.org/10.1002/num.22544
  • Kumar, K., Gupta, T., Pramod Chakravarthy, P., & Nageshwar Rao, R. (2019). An adaptive mesh selection strategy for solving singularly perturbed parabolic partial differential equations with a small delay. In. Applied Mathematics and Scientific Computing, Springer, 67–76. https://doi.org/10.1007/978-3-030-01123-9_8
  • Kumar, D., & Kadalbajoo, M. K. (2011). A parameter-uniform numerical method for time-dependent singularly perturbed differential-difference equations. Applied Mathematical Modelling, 35(6), 2805–2819. https://doi.org/10.1016/j.apm.2010.11.074
  • Kumar, D., & Kumari, P. (2019). A parameter-uniform numerical scheme for the parabolic singularly perturbed initial boundary value problems with large time delay. Journal of Applied Mathematics and Computing, 59(1), 179–206. https://doi.org/10.1007/s12190-018-1174-z
  • Kumar, D., & Kumari, P. (2020). Parameter-uniform numerical treatment of singularly perturbed initial-boundary value problems with large delay. Applied Numerical Mathematics, 153, 412–429. https://doi.org/10.1016/j.apnum.2020.02.021
  • Ladyzhenskaia, O. A., Solonnikov, V. A., & Ural’tseva, N. N. (1988). Linear and quasi-linear equations of parabolic type (Vol. 23). American Mathematical Soc.
  • Lange, C. G., & Miura, R. M. (1994). Singular perturbation analysis of boundary value problems for differential-difference equations. v. small shifts with rapid oscillations. SIAM Journal on Applied Mathematics, 54(1), 273–283. https://doi.org/10.1137/s0036139992228119
  • Manikandan, M., Shivaranjani, N., Miller, J. J. H., & Valarmathi, S. (2014). A parameter- uniform numerical method for a boundary value problem for a singularly perturbed delay differential equation. Advances in Applied Mathematics Springer 71–88. https://doi.org/10.1007/978-3-319-06923-4_7
  • Mickens, R. E. (1994). Nonstandard finite difference models of differential equations. world scientific.
  • Mukherjee, K., & Natesan, S. (2010, October). Richardson extrapolation technique for singularly perturbed parabolic convection–diffusion problems. Computing, 92(1), 1–32. https://doi.org/10.1007/s00607-010-0126-8
  • Musila, M., & Petr, L. (1991). Generalized stein’s model for anatomically complex neurons. BioSystems, 25(3), 179–191. https://doi.org/10.1016/0303-2647(91)90004-5
  • Negero, N. T., & Duressa, G. F. (2022). Uniform convergent solution of singularly perturbed parabolic differential equations with general temporal- lag. Iranian Journal of Science and Technology, Transactions A: Science, 46(2), 507–524. https://doi.org/10.1007/s40995-021-01258-2
  • Parthiban, S., Valarmathi, S., & Franklin, V. (2015). A numerical method to solve singularly perturbed linear parabolic second order delay differential equation of reaction-diffusion type. Malaya J Matematik, 412–420.
  • Prathap, T., & Nageshwar Rao, R. (2022). Uniformly convergent finite difference methods for singularly perturbed parabolic partial differential equations with mixed shifts. Journal of Applied Mathematics and Computing, 1–26. https://doi.org/10.1007/s12190-022-01802-2
  • Ramesh, V. P., & Kadalbajoo, M. K. (2008). Upwind and midpoint upwind difference methods for time-dependent differential difference equations with layer behavior. Applied Mathematics and Computation, 202(2), 453–471. https://doi.org/10.1016/j.amc.2007.11.033
  • Roos, H.-G., Stynes, M., & Tobiska, L. (2008). Robust numerical methods for singularly perturbed differential equations: Convection-diffusion-reaction and flow problems (Vol. 24). Springer Science & Business Media.
  • Stein, R. B. (1965). A theoretical analysis of neuronal variability. Biophysical Journal, 5(2), 173–194. https://doi.org/10.1016/S0006-3495(65)86709-1
  • Stein, R. B. (1967). Some models of neuronal variability. Biophysical Journal, 7(1), 37–68. https://doi.org/10.1016/S0006-3495(67)86574-3
  • Woldaregay, M. M., Duressa, G. F., & Scapellato, A. (2021). Uniformly convergent hybrid numerical method for singularly perturbed delay convection- diffusion problems. International Journal of Differential Equations, 2021, 1–20. https://doi.org/10.1155/2021/6654495