Open Access

Galerkin-Chebyshev Pseudo Spectral Method and a Split Step New Approach for a Class of Two dimensional Semi-linear Parabolic Equations of Second Order


Cite

Z. F. Tian and Y. B. Ge,1.(2007), A fourth-order compact ADI method for solving two-dimensional unsteady convection-diffusion problems, J. Comput. Appl. Math. 198, 268-286. 10.1016/j.cam.2005.12.005TianZ. F.GeB. Y.2007A fourth-order compact ADI method for solving two-dimensional unsteady convection-diffusion problemsJ. Comput. Appl. Math. 19826828610.1016/j.cam.2005.12.00510.1016/j.cam.2005.12.005Search in Google Scholar

A. Mohebbi and M. Dehghan,2.(2010), High-order compact solution of the one-dimensional heat and advection diffusion equations. Appl. Math. Model. 34, 3071-3084. 10.1016/j.apm.2010.01.01310.1016/j.apm.2010.01.013MohebbiA.DehghanM.2010High-order compact solution of the one-dimensional heat and advection diffusion equationsAppl. Math. Model.343071308410.1016/j.apm.2010.01.013Open DOISearch in Google Scholar

A. Lasis and E. Süli,3.(2007), hp-Version Discontinuous Galerkin Finite Element Methods for Semilinear Parabolic Problems, SIAM J. Numer. Anal.45(4), 1544-1569. 10.1137/05064212510.1137/050642125LasisA.SüliE.2007hp-Version Discontinuous Galerkin Finite Element Methods for Semilinear Parabolic ProblemsSIAM J. Numer. Anal.4541544156910.1137/050642125Open DOISearch in Google Scholar

C. Chen and W. Liu,4.(2010), Two-grid finite volume element methods for semilinear parabolic problems, Applied Numerical Mathematics, January-February, Volume 60, Issues 1-2, Pages 10-18. 10.1016/j.apnum.2009.08.00410.1016/j.apnum.2009.08.004ChenC.LiuW.2010Two-grid finite volume element methods for semilinear parabolic problemsApplied Numerical MathematicsJanuary-February601-2101810.1016/j.apnum.2009.08.004Open DOISearch in Google Scholar

W. Liu, J. Sun and B. Wu,5.(2016), Galerkin-Chebyshev spectral method and block boundary value methods for two-dimensional semilinear parabolic equations, Numer Algor. 71, 437-455. 10.1007/s110710.1007/s11075-015-0002-xLiuW.SunJ.WuB.2016Galerkin-Chebyshev spectral method and block boundary value methods for two-dimensional semilinear parabolic equationsNumer Algor.7143745510.1007/s1107Open DOISearch in Google Scholar

W. Geng and S. Zhao,6.(2013) Fully implicit ADI schemes for solving the nonlinear Poisson-Boltzmann equation, Molecular Based Math. Bio. 1, 109-123. 10.2478/mlbmb-2013-0006GengW.ZhaoS.2013Fully implicit ADI schemes for solving the nonlinear Poisson-Boltzmann equationMolecular Based Math. Bio.110912310.2478/mlbmb-2013-000610.2478/mlbmb-2013-0006Search in Google Scholar

B. Z. Lu, Y.C. Zhou, M.J. Holst and J.A. McCammon,7.(2008) Recent progress in numerical methods for the Poisson-Boltzmann equation in biophysical applications, Commun. Comput. Phys. 3, 973-1009.LuB. Z.ZhouY.C.HolstM.J.McCammonJ.A.2008Recent progress in numerical methods for the Poisson-Boltzmann equation in biophysical applicationsCommun. Comput. Phys.39731009Search in Google Scholar

W. Deng, X. Zhufu, J. Xu, and S. Zhao,8.(2015), A new discontinuous Galerkin method for the nonlinear Poisson-Boltzmann equation, Applied Mathematics Letters. 49, 126-132.10.1016/j.aml.2015.05.00810.1016/j.aml.2015.05.008DengW.ZhufuX.XuJ.ZhaoS.2015A new discontinuous Galerkin method for the nonlinear Poisson-Boltzmann equationApplied Mathematics Letters.4912613210.1016/j.aml.2015.05.008Open DOISearch in Google Scholar

J. Shen, T. Tang and L. Wang,9.(2011), Spectral Methods Algorithms, Analysis and Applications, Springer Series in Computational Mathematics, ISBN-10: 354071040X; ISBN-13: 978-3540710400.ShenJ.TangT.WangL.2011Spectral Methods Algorithms, Analysis and ApplicationsSpringer Series in Computational MathematicsISBN-10: 354071040X; ISBN-13: 978-3540710400.10.1007/978-3-540-71041-7Search in Google Scholar

S. Movahed, R. Kamali, M. Eghtesad and A. Khosravifard,10.(2013), Analytical study of mixed electroosmotic-pressure-driven flow in rectangular micro-channels, Theor. Comput. Fluid Dyn. 27, 599-616.10.1007/s00162-012-0283-910.1007/s00162-012-0283-9MovahedS.KamaliR.EghtesadM.KhosravifardA.2013Analytical study of mixed electroosmotic-pressure-driven flow in rectangular micro-channelsTheor. Comput. Fluid Dyn.2759961610.1007/s00162-012-0283-9Open DOISearch in Google Scholar

M. Reshadi, M. H. Saidi, B. Firoozabadi and M. S. Saidi,11.(2016), Electrokinetic and aspect ratio effects on secondary flow of viscoelastic fluids in rectangular microchannels, Microfluid Nanofluid. 20:117. 10.1007/s10404-016-1780-810.1007/s10404-016-1780-8ReshadiM.SaidiM. H.FiroozabadiB.SaidiM. S.2016Electrokinetic and aspect ratio effects on secondary flow of viscoelastic fluids in rectangular microchannelsMicrofluid Nanofluid.2011710.1007/s10404-016-1780-8Open DOISearch in Google Scholar

A. Sayyed-Ahmad, K. Tuncay, and P.J. Ortoleva,12.(2004), Efficient solution technique for solving the Poisson-Boltzmann equation. J. Comput. Chem. 25, 1068-1074. 10.1002/jcc.2003910.1002/jcc.2003915067682Sayyed-AhmadA.TuncayK.OrtolevaP.J.2004Efficient solution technique for solving the Poisson-Boltzmann equationJ. Comput. Chem.251068107410.1002/jcc.2003915067682Open DOISearch in Google Scholar

A.I. Shestakov, J.L. Milovich, and A. Noy,13.(2002) Solution of the nonlinear Poisson-Boltzmann equation using pseudotransient continuation and the finite element method. J. Colloid Interface Sci. 247, 62-79. 10.1006/jcis.2001.803310.1006/jcis.2001.8033ShestakovA.I.MilovichJ.L.NoyA.2002Solution of the nonlinear Poisson-Boltzmann equation using pseudotransient continuation and the finite element methodJ. Colloid Interface Sci.247627910.1006/jcis.2001.803316290441Open DOISearch in Google Scholar

S. Zhao,14.(2011), Pseudo-time coupled nonlinear models for biomolecular surface representation and solvation analysis. Int. J. Numer. Method Bio. Engrg.27, 1964-1981. 10.1002/cnm.145010.1002/cnm.1450ZhaoS.2011Pseudo-time coupled nonlinear models for biomolecular surface representation and solvation analysisInt. J. Numer. Method Bio. Engrg.271964198110.1002/cnm.1450Open DOISearch in Google Scholar

S. Zhao,15.(2014), Operator splitting ADI schemes for pseudo-time coupled nonlinear solvation simulations, Journal of Computational Physics. 257, 1000-1021. 10.1016/j.jcp.2013.09.04310.1016/j.jcp.2013.09.043ZhaoS.2014Operator splitting ADI schemes for pseudo-time coupled nonlinear solvation simulationsJournal of Computational Physics.2571000102110.1016/j.jcp.2013.09.043Open DOISearch in Google Scholar

eISSN:
2444-8656
Language:
English
Publication timeframe:
2 times per year
Journal Subjects:
Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics