Zitieren

[1] AHMED, N.—MATTHIES, G.—TOBISKA, L.—XIE, H.: Discontinuous Galerkin time stepping with local projection stabilization for transient convection-diffusion-reaction problems, Comput. Methods Appl. Mech. Engrg. 200 (2011), no. 21–22, 1747–1756,10.1016/j.cma.2011.02.003 Search in Google Scholar

[2] BROOKS, A. N.—HUGHES, T. J.R.: Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg. 32 (1982), 199–259.10.1016/0045-7825(82)90071-8 Search in Google Scholar

[3] CAI, X.—CAI, D. — LU, M.: Finite volume method for time-dependent convection diffusion large Reynolds number problem. In: Second International Conference on Information and Computing Science, 2009, (ICIC ’09), pp. 360–363, doi: 10.1109/ICIC.2009.296.10.1109/ICIC.2009.296 Search in Google Scholar

[4] CAI, X.—LIU, F.: A Reynolds uniform scheme for singularly perturbed parabolic differential equation, Anziam J. 47 (2005) (C), C 633-C 648.10.21914/anziamj.v47i0.1067 Search in Google Scholar

[5] CLAVERO, C.—JORGE, J. C.—LISBONA, F.: Uniformly convergent scheme on a nonuniform mesh for convection-diffusion parabolic problems, J. Comput. Appl. Math. 154 (2003), 415–429.10.1016/S0377-0427(02)00861-0 Search in Google Scholar

[6] CLAVERO, C.—GRACIA, J. L.—STYNES, M.:, A simpler analysis of a hybrid numerical method for time-dependent convection–diffusion problems, J. Comput. Appl. Math. 235 (2011), 5240–5248.10.1016/j.cam.2011.05.025 Search in Google Scholar

[7] CLAVERO, C.—JORGE, J. C.—LISBONA, F.—SHISHKIN, G.I.: A fractional step method on a special mesh for the resolution of multidimensional evolutionary convection-diffusion problems. Appl. Numer. Math. 27 (1998), no. 3, 211–231. Search in Google Scholar

[8] CLAVERO, C.—JORGE, J. C.—LISBONA, F.: Uniformly convergent schemes for singular perturbation problems combining alternating directions and exponential fitting techniques. In: (Miller J. J.H. ed.) Applications of Advanced Computational Methods for Boundary and Interior Layers. Adv. Comput. Methods Bound. Inter. Layers, 2, Boole Press, Dublin, 1993, pp. 33–52. Search in Google Scholar

[9] DE BOOR, C.: A Practical Guide to Splines. In: Applied Mathematical Sciences Vol. 27, Springer-Verlag, Berlin, 1978.10.1007/978-1-4612-6333-3 Search in Google Scholar

[10] DEB, R.—NATESAN, S.: Higher-order time accurate numerical methods for singularly perturbed parabolic partial differential equations, Int. J. Comput. Math. 86 (2009), no. 7, 1204–1214. Search in Google Scholar

[11] EL HAJAJI, A.—HILAL, K.—SERGHINI, A.—MERMRI, EL BEKKEY, M.: Pricing American bond options using a cubic spline collocation method. Bol. Soc. Parana. Mat, 32 (2014) no. 2, 189–208. Search in Google Scholar

[12] EL MERZGUIOUI, M.—EL HAJAJI, A.— HILAL, K.—CHADLI, L.S.: A numerical method for solving time-dependent convection-diffusion problems, Bol. Soc. Parana. Mat, (3) 35 (2017), no. 1, 217–228. Search in Google Scholar

[13] JICHUN LI: Uniform convergence of discontinuous finite element methods for singularly perturbed reaction-diffusion problems, Comput. Math. Appl. 44 (2002), no. 1–2, 231–240. Search in Google Scholar

[14] FRIEDMAN, A.: Partial Differential Equation of Parabolic Type. Robert E. Krieger Publishing Co., Huntington, NY, 1983. Search in Google Scholar

[15] JICHUN LI—NAVON, I. M.: Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: convection-diffusion type, Comput. Methods Appl. Mech. Engrg. 162 (1998), no. 1–4, 49–78. Search in Google Scholar

[16] HINDMARSH, A. C.—GRESHO, P. M.—GRIFFITHS, D. F.: The stability of explicit Euler time-integration for certain finite difference approximations of the multi-dimensional advection-diffusion equation, Int. J. Numer. Meth. Fluids 4 (1984), 853–897.10.1002/fld.1650040905 Search in Google Scholar

[17] HUGHES, T. J. R.—BROOKS, A.: A multidimensional upwind scheme with no crosswind diffusion, (T. J.R. Hughes, ed.) In: Finite Element Methods for Convection Dominated Flows, (Papers, Winter Ann. Meeting Amer. Soc. Mech. Engrs., New York, 1979), AMD Vol. 34, Amer. Soc. Mech. Engrs. (ASME), New York, 1979, pp. 19–35. Search in Google Scholar

[18] KADALBAJOO, M. K.—TRIPATHI, L. P.—KUMAR, A.: A cubic B-spline collocation for a numerical solution of generalized Black-Scholes equation, Math. Comput. Modelling 55 (2012), no. 3–4, 1483–1505. Search in Google Scholar

[19] KUZMIN, D.: Explicit and implicit FEM-FCT algorithms with flux linearization, J. Comput. Phys. 228 (2009), no. 7, 2517–2534. Search in Google Scholar

[20] KUZMIN, D— MÖLLER, M.—TUREK, S.: High–resolution FEM-FCT schemes for multidimensional conservation laws, Comput. Methods Appl. Mech. Engrg. 193 (2004), 4915–4946.10.1016/j.cma.2004.05.009 Search in Google Scholar

[21] LADYZENSKAJA, Ö. A.—SOLONNIKOV, V. A.—URAL’CEVA, N. N.: Linear and Quasilinear Equations of Parabolic Type. In: Amer. Math. Soc. Transl. Vol. 23, Providence, RI. 1968. Search in Google Scholar

[22] EL BEKKEY MERMRI.—SERGHINI, A.—EL HAJAJI, A.—HILAL, K. : A Cubic Spline Method for Solving a Unilateral Obstacle Problem, American J. Comput. Math. 2 (2012), no. 3, doi: 10.4236/ajcm.2012.23028.10.4236/ajcm.2012.23028 Search in Google Scholar

[23] LI, JICHUN: High-order finite difference schemes for differential equations containing higher derivatives, Appl. Math. Comput. 171 (2005), no. 2, 1157–1176. Search in Google Scholar

[24] MITCHELL, A. R.—GRIFFITHS, D. F.: Upwinding by Petrov-Galerkin methods in convection-diffusion problems, J. Comput. Appl. Math. 6 (1980), 219–228.10.1016/0771-050X(80)90029-7 Search in Google Scholar

[25] KADALBAJOO, MOHAN, K.—YADAW, A. S.: B-Spline collocation method for a two-parameter singularly perturbed convection-diffusion boundary value problems, Appl. Math. and Comput. 201 (2008), no. 1–2, 504–513. Search in Google Scholar

[26] NATESAN, S.—DEB, R.: A robust numerical scheme for singularly perturbed parabolic reaction diffusion problems, Neural Parallel Sci. Comput. 16 (2008), no. 3, 419–433. Search in Google Scholar

[27] NG-STYNES, M. J.—O’RIORDAN, E.—STYNES, M.: Numerical methods for time-dependent convection-diffusion equations, J. Comput. Appl. Math. 21 (1988), no. 3, 289–310. Search in Google Scholar

[28] LI, JICHUN: Convergence and superconvergence analysis of finite element methods on highly nonuniform anisotropic meshes for singularly perturbed reaction-diffusion problems, Appl. Numerical Math. 36 (2001), no. 2–3, 129–154. Search in Google Scholar

[29] RAMOS, J.I.: (2005) An exponentially fitted method for singularly perturbed, one-dimensional, parabolic problems, Appl. Math. Comput. 161 (2005), 513–523.10.1016/j.amc.2003.12.046 Search in Google Scholar

[30] ROOS, H.-G.—STYNES, M.—TOBISKA, L.: Robust Numerical Methods for Singularly Perturbed Differential Equations Convection-diffusion-reaction and Flow Problems. (2nd edition). In: Springer Series in Computational Mathematics, Vol. 24, Springer-Verlag, Berlin, 2008. Search in Google Scholar

[31] LI, JICHUN: Finite element analysis for a nonlinear diffusion model in image processing, Appl. Math. Lett. 15 (2002), no. 2, 197–202. Search in Google Scholar

[32] SURLA, K.—TEOFANOV, L.—UZELAC, Z.: A robust layer-resolving spline collocation method for a convection-diffusion problem, Appl. Math. Comput. 208 (2009), no. 1, 76–89. Search in Google Scholar

[33] SURLA, K.—JERKOVIĆ, V.: Some possibilities of applying spline collocations to singular perturbation problems. In: Numerical Methods and Approximation Theory, Vol. II, Univ. Novi Sad, Novi Sad, 1985. pp. 19–25. Search in Google Scholar

[34] YU, C. C.—HEIMICH, J. C.: Petrov-Galerkin methods for the time-dependent convective transport equation, Internat. J. Numer. Methods Engrg. 23 (1986), 883–901.10.1002/nme.1620230510 Search in Google Scholar

[35] ZHANG, J.—YANG, D.: (2011) Parallel least-squares finite element method for time dependent convection-diffusion system, Computing 91 (2011), no. 3, 217–240. Search in Google Scholar

[36] ZHU, P.—XIE, Z.—ZHOU, S.: A uniformly convergent continuous–discontinuous Galerkin method for singularly perturbed problems of convection-diffusion type, Appl. Math. Comput. 217 (2011), no. 9, 4781–4790. Search in Google Scholar

eISSN:
1338-9750
Sprache:
Englisch
Zeitrahmen der Veröffentlichung:
3 Hefte pro Jahr
Fachgebiete der Zeitschrift:
Mathematik, Allgemeines