Acknowledgement
This work was supported by the research grant of College of Natural Sciences, Jimma University
References
- M. Adilaxmi, D. Bhargavi and Y.N. Reddy, An initial value technique using exponentially fitted non standard finite difference method for singularly perturbed differential difference equations, Applications and applied Mathematics 14 (2019), 245-269.
- M. Bahgat and M.A. Hafiz, Numerical Solution of Singularly Perturbed Two-Parameters DDE using Numerical Integration Method, European Journal of Scientific Research 122 (2014), 36-44.
- M. Bestehorn and E.V. Grigorieva, Formation and propagation of localized states in extended systems, Ann. Phys. 13 (2004), 423-431. https://doi.org/10.1002/andp.200410085
- G.F. Duressa and Y.N. Reddy, Domain decomposition method for singularly perturbed differential difference equations with layer behaviour, International Journal of Engineering & Applied Sciences 7 (2015), 86-102. https://doi.org/10.24107/ijeas.251236
- D.D. Joseph and L. Preziosi, Heat waves, Rev. Mod. Phys. 61 (1989), 41-73. https://doi.org/10.1103/RevModPhys.61.41
- M.K. Kadalbajoo and V.P. Ramesh, Numerical methods on Shishkin mesh for singularly perturbed delay differential equations with a grid adaptation strategy, Applied Mathematics and Computation 188 (2007), 1816-1831. https://doi.org/10.1016/j.amc.2006.11.046
- T. Kellogg and A. Tsan, Analysis of some difference approximations for a singular perturbation problem without turning point, Math. Comput. 32 (1978), 1025-1039. https://doi.org/10.1090/S0025-5718-1978-0483484-9
- D. Kumar and M.K. Kadalbajoo, Numerical treatment of singularly perturbed delay differential equations using B-Spline collocation method on Shishkin mesh, Journal of Numerical Analysis, Industrial and Applied Mathematics 7 (2012), 73-90.
- C.G. Lange and R.M. Miura, Singular perturbation analysis of boundary value problems for differential-difference equations, SIAM Journal on Applied Mathematics 42 (1982), 502-531. https://doi.org/10.1137/0142036
- Q. Liu, X. Wang and D.D. Kee, Mass transport through swelling membranes, Int. J. Eng. Sci. 43 (2005), 1464-1470. https://doi.org/10.1016/j.ijengsci.2005.05.010
- M.C. Mackey and L. Glass, Oscillations and chaos in physiological control systems, Science 197 (1977), 287-289. https://doi.org/10.1126/science.267326
- W.G. Melesse, A.A. Tiruneh, and G.A. Derese, Solving second order singularly perturbed delay differential equations with layer behavior via initial value method, J. Appl. Math. & Informatics 36 (2018), 331-348. https://doi.org/10.14317/JAMI.2018.331
- W.G. Melesse, A.A. Tiruneh, and G.A. Derese, Fitted mesh method for singularly perturbed delay differential turning point problems exhibiting twin boundary layers, J. Appl. Math. & Informatics 38 (2020), 113-132. https://doi.org/10.14317/jami.2020.113
- J,J.H. Miller, E. O'Riordan and G.I. Shishkin, Fitted numerical methods for singular perturbation problems: error estimates in the maximum norm for linear problems in one and two dimensions, World Scientific, Singapore, 2012.
- R.E. O'Malley, Singular perturbation methods for ordinary differential equations, Springer Science, New York, 1991.
- K. Phaneendra and M. Lalu, Numerical solution of singularly perturbed delay differential equations using gaussion quadrature method, IOP Journal Physics. Conference Series 1344 (2019), 1-13.
- H. Tian, The exponential asymptotic stability of singularly perturbed delay differential equations with a bounded lag, J. Math. Anal. Appl. 270 (2002), 143-149. https://doi.org/10.1016/S0022-247X(02)00056-2
- D.Y. Tzou, Micro-to-macro scale Heat Transfer, Taylor & Francis, Washington DC, 1997.
- M. Wazewska-Czyzewska and A. Lasota, Mathematical models of the red cell system, Mat. Stos. 6 (1976), 25-40.
- M.M. Woldaregay and G.F. Duressa, Parameter uniform numerical method for singularly perturbed differential difference equations, J. Nigerian Math. Soc. 38 (2019), 223-245.
- M.M. Woldaregay and G.F. Duressa, Uniformly convergent numerical method for singularly perturbed delay parabolic differential equations arising in computational neuroscience, Kragujevac J. Math. 46 (2022), 65-84.
- M.M. Woldaregay and G.F. Duressa, Fitted Numerical Scheme for Singularly Perturbed Differential Equations Having Small Delays, Caspian Journal of Mathematical Sciences 10 (2021), in press.
- M.M. Woldaregay and G.F. Duressa, Robust Numerical Scheme for Solving Singularly Perturbed Differential Equations Involving Small Delays, Applied Mathematics E-Notes 2020 (2020), in press.
- M.M. Woldaregay and G.F. Duressa, Higher-Order Uniformly Convergent Numerical Scheme for Singularly Perturbed Differential Difference Equations with Mixed Small Shifts, International Journal of Differential Equations 2020 (2020), 1-15.