Exponential methods for one-dimensional reaction-diffusion equations

Applied Mathematics and Computation

Volumn 170, Issue 1, 2005, Pages 380-398

  Ramos, J I ^a  

^a UNIVERSITY OF MÁLAGA   (Spain)

Author keywords

Exponential methods; Fisher equation; Nagumo equation; One dimensional reaction diffusion equations; Quasilineraization; Time linearization

Indexed keywords

FINITE DIFFERENCE METHOD; ITERATIVE METHODS; MATHEMATICAL OPERATORS; ORDINARY DIFFERENTIAL EQUATIONS;

EXPONENTIAL METHODS; FISHER EQUATION; NAGUMO EQUATION; ONE-DIMENSIONAL REACTION-DIFFUSION REACTIONS; QUASILINEARIZATION; TIME LINEARIZATION;

NONLINEAR EQUATIONS;

EID: 26844477547     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.12.003     Document Type: Article

References (11)

1. J.I. Ramos Numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory T.C. Chawla Annual Review of Numerical Fluid Mechanics and Heat Transfer vol. 1 1987 Hemisphere Publishing Corporation New York 150 261 (Chapter 4)
2. J.I. Ramos Finite element methods for one-dimensional flame propagation problems T.J. Chung Numerical Modeling in Combustion 1993 Taylor & Francis Washington, DC 3 131 (Chapter 1)
3. Z. Chen, A.B. Gumel, and R.E. Mickens Nonstandard discretizations of the generalized Nagumo reaction-diffusion equation Numerical Methods for Partial Differential Equations 19 2003 363 379
4. R.E. Mickens A best finite-difference scheme for the Fisher equation Numerical Methods for Partial Differential Equations 10 1994 581 585
5. O.O. Onyejekwe Green element procedures for transport accompanied by nonlinear reaction International Journal of Thermal Sciences 42 2003 813 820
6. R.E. Mickens Nonstandard Finite Difference Models of Differential Equations 1994 World Scientific Singapore
7. R.E. Mickens Applications of Nonstandard Finite-Difference Schemes 2000 World Scientific River Edge, NJ
8. Rizwan-Uddin Comparison of the nodal integral method and nonstandard finite-difference schemes for the Fisher equation SIAM Journal of Scientific Computing 22 2001 1926 1942
9. J.I. Ramos On diffusive and exponentially fitted techniques Applied Mathematics and Computation 103 1999 69 96
10. J.I. Ramos Linearization methods for reaction-diffusion equations: multidimensional problems Applied Mathematics and Computation 88 1997 225 254
11. J.I. Ramos Linearized factorization techniques for multidimensional reaction-diffusion equations Applied Mathematics and Computation 100 1999 201 222