Open Access

A Numerical Scheme For Semilinear Singularly Perturbed Reaction-Diffusion Problems


Cite

R. E. O'Malley Jr., Singular Perturbation Methods for Ordinary Differential Equations, Springer-Verlag, New York, 1991.O'MalleyR. E.Jr.Singular Perturbation Methods for Ordinary Differential EquationsSpringer-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.Uniform Numerical Methods for Problems with Initial and Boundary LayersBoole, 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.Robust Computational Techniques for Boundary LayersChapman-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 problemsZAMM Z Angew Math Mech78199829130910.1002/(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.Numerical Methods for Singularly Perturbed Differential Equations, Convection-Diffusion and Flow ProblemsSpringer 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.Fitted Numerical Methods for Singular Perturbation Problems, Error Estimates in the Maximum Norm for Linear Problems in One and Two DimensionsWorld 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 EquationsTr. J. of Mathematics1931995207222Search 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 systemApplied Mathematics and Computation162320051023103410.1016/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 equationsNumer. Algorithms524200966367510.1007/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.Theory of difference schemesMonographs 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 LayersApplied Mathematics and Information Sciences432010341352Search 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 ProblemsJournal of Comp. And Applied Mathematics230201026026910.1016/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 problemsApplied Math. and Comp.171200554756610.1016/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, nternationalJournal of Computer Math.843200731732310.1080/00207160601138913Search 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 ProblemsNumerical Algorithms402005233210.1007/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 ProblemsApplied Numerical Mathematics612011385210.1016/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 SolutionsComputers and Mathematics with Applications51200685786410.1016/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 ProblemsApplied Numerical Mathematics612011385210.1016/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 ProblemsHundawi Publishing Corporation, Mathematical Problems in Engineering2012Article 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 solutionsApplied Numerical Mathematics512–3200427328810.1016/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 problemApplied Mathematics Letters232010122112250z010.1016/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.Numerical Analysis(In Turkish)I. EditionSeckin PublicationsAnkara2018Search in Google Scholar

eISSN:
2444-8656
Language:
English
Publication timeframe:
Volume Open
Journal Subjects:
Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics