×
Ayele, Mulunesh Amsalu; Tiruneh, Awoke Andargie; Derese, Getachew Adamu

Hybrid fitted numerical scheme for singularly perturbed convection-diffusion problem with a small time lag. (English) Zbl 1522.76041

Abstr. Appl. Anal. 2023, Article ID 4382780, 15 p. (2023).

Cited in 1 Document

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
Cite Review PDF
Full Text: DOI
OA License

References:

[1] Arino, J.; Van Den Driessche, P., Time delays in epidemic models, Delay differential equations and applications, 539-578 (2006), Springer · Zbl 1131.34055
[2] Bejan, A., Convection Heat Transfer (2013), New York: Wiley, New York
[3] Cooke, K.; Van den Driessche, P.; Zou, X., Interaction of maturation delay and nonlinear birth in population and epidemic models, Journal of Mathematical Biology, 39, 4, 332-352 (1999) · Zbl 0945.92016 · doi:10.1007/s002850050194
[4] Murray, J. D., Mathematical Biology: I. An introduction (2002), Springer · Zbl 1006.92001 · doi:10.1007/b98868
[5] Vielle, B.; Chauvet, G., Delay equation analysis of human respiratory stability, Mathematical Biosciences, 152, 2, 105-122 (1998) · Zbl 0930.92006 · doi:10.1016/S0025-5564(98)10028-7
[6] Villasana, M.; Radunskaya, A., A delay differential equation model for tumor growth, Journal of Mathematical Biology, 47, 3, 270-294 (2003) · Zbl 1023.92014 · doi:10.1007/s00285-003-0211-0
[7] Das, A.; Natesan, S., Uniformly convergent hybrid numerical scheme for singularly perturbed delay parabolic convection-diffusion problems on Shishkin mesh, Applied Mathematics and Computation, 271, 168-186 (2015) · Zbl 1410.65305 · doi:10.1016/j.amc.2015.08.137
[8] Kumar, D.; Kumari, P., 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, 1-2, 179-206 (2019) · Zbl 1418.65101 · doi:10.1007/s12190-018-1174-z
[9] Cimen, E., Numerical solution of a boundary value problem including both delay and boundary layer, Mathematical Modelling and Analysis, 23, 4, 568-581 (2018) · Zbl 1488.65190 · doi:10.3846/mma.2018.034
[10] Cimen, E.; Amiraliyev, G. M., Uniform convergence method for a delay differential problem with layer behaviour, Mediterranean Journal of Mathematics, 16, 3 (2019) · Zbl 1483.65110 · doi:10.1007/s00009-019-1335-9
[11] Gebeyaw, W.; Andargie, A.; Adamu, G., Solving second order singularly perturbed delay differential equations with layer behavior via initial value method, Journal of Applied Mathematics & Informatics, 36, 34, 331-348 (2018) · Zbl 1403.65030
[12] Melesse, W. G.; Tiruneh, A. A.; Derese, G. A., Solving linear second-order singularly perturbed differential difference equations via initial value method, International Journal of Differential Equations, 2019 (2019) · Zbl 1447.34061 · doi:10.1155/2019/5259130
[13] Woldaregay, M. M., Solving singularly perturbed delay differential equations via fitted mesh and exact difference method, Research in Mathematics, 9, 1, article 2109301 (2022) · doi:10.1080/27684830.2022.2109301
[14] Govindarao, L.; Mohapatra, J., A second order numerical method for singularly perturbed delay parabolic partial differential equation, Engineering Computations, 36, 2, 420-444 (2019) · doi:10.1108/EC-08-2018-0337
[15] Podila, P. C.; Kumar, K., A new stable finite difference scheme and its convergence for time-delayed singularly perturbed parabolic pdes, Computational and Applied Mathematics, 39, 3 (2020) · Zbl 1449.65198
[16] Woldaregay, M. M.; Aniley, W. T.; Duressa, G. F., Novel numerical scheme for singularly perturbed time delay convection- diffusion equation, Advances in Mathematical Physics, 2021 (2021) · Zbl 1481.65164 · doi:10.1155/2021/6641236
[17] Kumar, K.; Gupta, T.; Pramod Chakravarthy, P.; Nageshwar Rao, R., An adaptive mesh selection strategy for solving singularly perturbed parabolic partial differential equations with a small delay, Applied Mathematics and Scientific Computing, 67-76 (2019), Springer · Zbl 1465.65074 · doi:10.1007/978-3-030-01123-9_8
[18] Negero, N. T.; Duressa, G. F., 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 (2022) · doi:10.1007/s40995-021-01258-2
[19] Tesfaye, S. K.; Woldaregay, M. M.; Dinka, T. G.; Duressa, G. F., Fitted computational method for solving singularly perturbed small time lag problem, BMC Research Notes, 15, 1, 318 (2022) · doi:10.1186/s13104-022-06202-0
[20] Salama, A.; Al-Amery, D., A higher order uniformly convergent method for singularly perturbed delay parabolic partial differential equations, International Journal of Computer Mathematics, 94, 12, 2520-2546 (2017) · Zbl 1398.65185 · doi:10.1080/00207160.2017.1284317
[21] Kadalbajoo, M.; Sharma, K., Numerical treatment of a mathematical model arising from a model of neuronal variability, Journal of Mathematical Analysis and Applications, 307, 2, 606-627 (2005) · Zbl 1062.92012 · doi:10.1016/j.jmaa.2005.02.014
[22] Govindarao, L.; Mohapatra, J., Numerical analysis and simulation of delay parabolic partial differential equation involving a small parameter, Engineering Computations, 37, 1, 289-312 (2019) · doi:10.1108/EC-03-2019-0115
[23] Mushahary, P.; Sahu, S. R.; Mohapatra, J., Spline approximation method for singularly perturbed differential-difference equation on nonuniform grids, International Journal of Modeling, Simulation, and Scientific Computing, 12, 1, article 2150005 (2021) · doi:10.1142/S1793962321500057
[24] Majumdar, A.; Natesan, S., Anϵ-uniform hybrid numerical scheme for a singularly perturbed degenerate parabolic convection-diffusion problem, International Journal of Computer Mathematics, 96, 7, 1313-1334 (2019) · Zbl 1499.65414 · doi:10.1080/00207160.2018.1485896
[25] Miller, J.; O’Riordan, E.; Shishkin, G., Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions (2012), World Scientific · Zbl 1243.65002 · doi:10.1142/8410
[26] Priyadharshini, R. M.; Ramanujam, N.; Valanarasu, T., Hybrid difference schemes for singularly perturbed problem of mixed type with discontinuous source term, Journal of Applied Mathematics & Informatics, 28, 56, 1035-1054 (2010) · Zbl 1278.65113
[27] Stynes, M.; Roos, H.-G., The midpoint upwind scheme, Applied Numerical Mathematics, 23, 3, 361-374 (1997) · Zbl 0877.65055 · doi:10.1016/S0168-9274(96)00071-2
[28] Mushahary, P.; Sahu, S.; Mohapatra, J., A parameter uniform numerical scheme for singularly perturbed differential-difference equations with mixed shifts, Journal of Applied and Computational Mechanics, 6, 2, 344-356 (2020)
[29] Bawa, R. K.; Natesan, S., An efficient hybrid numerical scheme for convection-dominated boundary-value problems, International Journal of Computer Mathematics, 86, 2, 261-273 (2009) · Zbl 1158.65330 · doi:10.1080/00207160801955678
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.