Linearly-implicit, approximate factorization, exponential methods for multi-dimensional reaction-diffusion equations

Applied Mathematics and Computation

Volumn 174, Issue 2, 2006, Pages 1609-1633

  Ramos, J I ^a  

^a UNIVERSITY OF MÁLAGA   (Spain)

Author keywords

Approximate factorization; Linearly implicit techniques; Piecewise exponential solutions; Reaction diffusion equations; Rothe's methods

Indexed keywords

BOUNDARY VALUE PROBLEMS; MATHEMATICAL OPERATORS; ORDINARY DIFFERENTIAL EQUATIONS;

REACTION-DIFFUSION EQUATION; ROTHE'S METHODS; TWO-POINT BOUNDARY-VALUE PROBLEMS;

APPROXIMATION THEORY;

EID: 33644596197     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.07.020     Document Type: Article

References (25)

1. W.R. Briley, and H. McDonald On the structure and use of linearized block implicit methods J. Comput. Phys. 34 1980 54 73
2. W.R. Briley, and H. McDonald An overview and generalization of implicit Navier-Stokes algorithms and approximate factorization Comput. Fluids 30 2001 807 828
3. R.M. Beam, and R.F. Warming An implicit finite-difference algorithm for hyperbolic systems in conservation-law form J. Comput. Phys. 22 1976 87 110
4. R.M. Beam, and R.F. Warming An implicit factored scheme for the compressible Navier-Stokes equations AIAA J. 16 1978 393 402
5. J.I. Ramos Linearization methods for reaction-diffusion equations: 1-D problems Appl. Math. Comput. 88 1997 199 224
6. J.I. Ramos Linearization methods for reaction-diffusion equations: multidimensional problems Appl. Math. Comput. 88 1997 225 254
7. J.I. Ramos Linearized factorization techniques for multidimensional reaction-diffusion equations Appl. Math. Comput. 100 1999 201 222
8. J.I. Ramos Implicit, compact, linearized θ-methods with factorization for multidimensional reaction-diffusion equations Appl. Math. Comput. 94 1998 17 43
9. Y. Gu, W. Liao, and J. Zhu An efficient high-order algorithm for solving systems of 3-D reaction-diffusion equations J. Comput. Appl. Math. 155 2003 1 17
10. W. Liao, J. Zhu, and A.Q.M. Khaliq An efficient high-order algorithm for solving systems of reaction-diffusion equations Numer. Meth. Partial Diff. Equat. 18 2002 340 354
11. J.I. Ramos On diffusive methods and exponentially-fitted techniques Appl. Math. Comput. 103 1999 69 96
12. J.I. Ramos, Exponential methods for one-dimensional reaction-diffusion equations, Appl. Math. Comput., in press, doi:10.1016/j.amc.2004.12.003.
13. D. Britz, O. Østerby, and J. Strutwolf Damping of Crank-Nicolson error oscillations Comput. Biol. Chem. 27 2003 253 263
14. O. Østerby Five ways of reducing the Crank-Nicolson oscillations BIT 43 2003 811 822
15. J.I. Ramos, Exponential numerical methods for one-dimensional, one-phase Stefan problems, Arch. Appl. Mech., in press.
16. E. Rothe Zweidimensionale parabolische Randwertaufgaben als eindimensionaler Randwertaufgaben Math. Ann. 102 1930 652 670
17. A. Ashyralyev, and P.E. Sobolevskii Well-posedness of Parabolic Difference Equations 1994 Birkhäuser Verlag Basel, Switzerland
18. N. Samec, and L. Škerget Integral formulation of a diffusive-convective transport equation for racting flows Eng. Anal. Bound. Elem. 28 2004 1055 1060
19. J.L. Mueller, and T.S. Shores A new sinc-Galerkin method for convection-diffusion equations with mixed boundary conditions Comput. Math. Appl. 47 2004 803 822
20. F. Schmidt, and D. Yevick Discrete boundary conditions for Schrödinger-type equations J. Comput. Phys. 134 1997 96 107
21. J. Lang High-resolution self-adaptive computations on chemical reaction-diffusion problems with internal boundaries Chem. Eng. Sci. 51 1996 1055 1070
22. E.N. Aksan, and A. Özdeş A numerical solution of Burgers' equation Appl. Math. Comput. 156 2004 395 402
23. T.W.H. Sheu, S.K. Wang, and R.K. Lin An implicit scheme for solving the convection-diffusion-reaction equation in two dimensions J. Comput. Phys. 164 2000 123 142
24. K.W. Morton Numerical Solution of Convection-Diffusion Problems 1996 Chapman & Hall London, UK
25. P.J. van der Houwen, and B.P. Sommeijer Approximate factorization for time-dependent partial differential equations J. Comput. Appl. Math. 128 2001 447 466