This work is licensed under the Creative Commons Attribution 4.0 International License.
R. E. O'Malley Jr., Singular Perturbation Methods for Ordinary Differential Equations, Springer-Verlag, New York, 1991.O'MalleyR. E.Jr.Springer-VerlagNew York199110.1007/978-1-4612-0977-5Search in Google Scholar
E. R. Doolan, J.J.H. Miller, and W. H. A. Schilders, Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole, Press, Dublin, 1980.DoolanE. R.MillerJ.J.H.SchildersW. H. A.Boole, PressDublin1980Search in Google Scholar
P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O’Riordan and G.I. Shishkin, Robust Computational Techniques for Boundary Layers; Chapman-Hall/CRC, New York, 2000.FarrellP.A.HegartyA.F.MillerJ.J.H.O’RiordanE.ShishkinG.I.Chapman-Hall/CRCNew York200010.1201/9781482285727Search in Google Scholar
H.-G. Roos, Layer-adapted grids for singular perturbation problems, ZAMM Z Angew Math Mech 78 (1998), 291–309.RoosH.-G.Layer-adapted grids for singular perturbation problems78199829130910.1002/(SICI)1521-4001(199805)78:5<291::AID-ZAMM291>3.0.CO;2-RSearch in Google Scholar
H.G. Roos, M. Stynes and L. Tobiska, Numerical Methods for Singularly Perturbed Differential Equations, Convection-Diffusion and Flow Problems, Springer Verlag, Berlin, 1996.RoosH.G.StynesM.TobiskaL.Springer VerlagBerlin199610.1007/978-3-662-03206-0Search in Google Scholar
J. H. Miller, E. O'Riordan, 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, 1996.MillerJ. H.O'RiordanE.ShishkinG. I.World ScientificSingapore199610.1142/2933Search in Google Scholar
G.M. Amiraliyev, Y.D, Mamedov, Differences Schemes on the Uniform Mesh for Singular Perturbed Pseudo-Parabolic Equations, Tr. J. of Mathematics, 19, 3 (1995), 207–222.AmiraliyevG.M.MamedovY.DDifferences Schemes on the Uniform Mesh for Singular Perturbed Pseudo-Parabolic Equations1931995207222Search in Google Scholar
G.M. Amiraliyev, The convergence of a finite difference method on layer-adapted mesh for a singularly perturbed system, Applied Mathematics and Computation, 162, 3 (2005) 1023–1034.AmiraliyevG.M.The convergence of a finite difference method on layer-adapted mesh for a singularly perturbed system162320051023103410.1016/j.amc.2004.01.015Search in Google Scholar
G.M. Amiraliyev, F. Erdogan, Difference schemes for a class of singularly perturbed initial value problems for delay differential equations, Numer. Algorithms, 52, 4 (2009) 663–675.AmiraliyevG.M.ErdoganF.Difference schemes for a class of singularly perturbed initial value problems for delay differential equations524200966367510.1007/s11075-009-9306-zSearch in Google Scholar
Samarskii A.A., Theory of difference schemes. Monographs and textbooks in pure and applied mathematics v 240. Marcel Dekker, New York, 761., 2001.SamarskiiA.A.Monographs and textbooks in pure and applied mathematics v 240.Marcel DekkerNew York761200110.1201/9780203908518Search in Google Scholar
K. Phaneendra, P. Pramod Chakravarthy, Y. N. Reddy, A Fitted Numerov Method for Singular Perturbation Problems Exhibiting Twin Layers, Applied Mathematics and Information Sciences 4, 3, (2010) 341–352.PhaneendraK.Pramod ChakravarthyP.ReddyY. N.A Fitted Numerov Method for Singular Perturbation Problems Exhibiting Twin Layers432010341352Search in Google Scholar
Holevoet, D., Daele, M.V., Berghe, G.V., The Optimal Exponentially-Fitted Numerov Method for Solving Two-Point Boundary Value Problems. Journal of Comp. And Applied Mathematics, 230, (2010) 260–269.HolevoetD.DaeleM.V.BergheG.V.The Optimal Exponentially-Fitted Numerov Method for Solving Two-Point Boundary Value Problems230201026026910.1016/j.cam.2008.11.011Search in Google Scholar
K.C. Patidar, High order fitted operator numerical method for self-adjoint singular perturbation problems, Applied Math. and Comp. 171 (2005) 547–566.PatidarK.C.High order fitted operator numerical method for self-adjoint singular perturbation problems171200554756610.1016/j.amc.2005.01.069Search in Google Scholar
R.K. Bawa, A Paralel aproach for self-adjoint singular perturbation problems using Numerov’s scheme, nternational Journal of Computer Math. Vol. 84, No. 3 (2007) 317–323.BawaR.K.A Paralel aproach for self-adjoint singular perturbation problems using Numerov’s scheme, nternational843200731732310.1080/00207160601138913Search in Google Scholar
Linss, T., Sufficient Conditions for Uniform Convergence on LAyer-Adapted Meshes for One-Dimentional Reaction-Diffusion Problems. Numerical Algorithms, 40 :(2005) 23–32.LinssT.Sufficient Conditions for Uniform Convergence on LAyer-Adapted Meshes for One-Dimentional Reaction-Diffusion Problems402005233210.1007/s11075-005-2265-0Search in Google Scholar
Wang, Y.M., On Numerov’s Method for a Class of Strongly Nonlinear Two-Point Boundary Value Problems, Applied Numerical Mathematics, 61, (2011) 38–52.WangY.M.On Numerov’s Method for a Class of Strongly Nonlinear Two-Point Boundary Value Problems612011385210.1016/j.apnum.2010.08.003Search in Google Scholar
Stynes, M., Kopteva, N., Numerical Analysis of Singularly Perturbed Nonlinear Reaction-Diffusion Problems with Multiple Solutions. Computers and Mathematics with Applications, 51 : (2006) 857–864.StynesM.KoptevaN.Numerical Analysis of Singularly Perturbed Nonlinear Reaction-Diffusion Problems with Multiple Solutions51200685786410.1016/j.camwa.2006.03.013Search in Google Scholar
Wang, Y.M., On Numerov’s Method for a Class of Strongly Nonlinear Two-Point Boundary Value Problems. Applied Numerical Mathematics, 61 :(2011) 38–52.WangY.M.On Numerov’s Method for a Class of Strongly Nonlinear Two-Point Boundary Value Problems612011385210.1016/j.apnum.2010.08.003Search in Google Scholar
Wang, Y.M., Wu, W.J., and Scalia, M., Numerov’s Method for a Class of Nonlinear Multipoint Boundary Value Problems. Hundawi Publishing Corporation, Mathematical Problems in Engineering, (2012) : Article ID 316852, 29pp.WangY.M.WuW.J.ScaliaM.Numerov’s Method for a Class of Nonlinear Multipoint Boundary Value Problems2012Article ID 316852,2910.1155/2012/316852Search in Google Scholar
Kopteva, N., Stynes, M., Numerical analysis of a singularly perturbed nonlinear reaction–diffusion problem with multiple solutions. Applied Numerical Mathematics, 51: 2–3, (2004) 273–288.KoptevaN.StynesM.Numerical analysis of a singularly perturbed nonlinear reaction–diffusion problem with multiple solutions512–3200427328810.1016/j.apnum.2004.07.001Search in Google Scholar
I.G. Amiraliyeva, F. Erdogan, G.M. Amiraliyev, A uniform numerical method for dealing with a singularly perturbed delay inital value problem. Applied Mathematics Letters, 23: (2010) 1221–1225. 0z0AmiraliyevaI.G.ErdoganF.AmiraliyevG.M.A uniform numerical method for dealing with a singularly perturbed delay inital value problem232010122112250z010.1016/j.aml.2010.06.002Search in Google Scholar
G.M. Amirali, I. Amirali, Numerical Analysis(In Turkish); I. Edition, Seckin Publications, Ankara, 2018.AmiraliG.M.AmiraliI.I. EditionSeckin PublicationsAnkara2018Search in Google Scholar