Numerical studies of a nonlinear heat equation with square root reaction term

Numerical Methods for Partial Differential Equations

Volumn 25, Issue 3, 2009, Pages 598-609

  Buckmire, Ron ^a   McMurtry, Karl ^a   Mickens, Ronald E ^b  

^a OCCIDENTAL COLLEGE   (United States)

^b CLARK ATLANTA UNIVERSITY   (United States)

Author keywords

Mickens discretization; Nonlinear heat equation; Nonstandard finite difference scheme; Numerical solutions; Positivity

Indexed keywords

EID: 66049150448     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20361     Document Type: Article

References (10)

1. 1 H. Wilhemsson, M. Benda, B. Etlicher, R. Jancel, and T. Lehner, Non‐linear evolution of densities in the presence of simultaneous diffusion and reaction processes, Phys Scripta 38 (1988), 863–874.
2. 2 R. Buckmire, Application of Mickens finite differences to several related boundary value problems, R. E. Mickens, editors, Advances in the applications of nonstandard finite difference schemes, World Scientific Publishing, Singapore, 2005, pp. 47–87.
3. 3 R. E. Mickens and A. Smith, Finite‐difference models of ordinary differential equations: influence of denominator functions, J Franklin Inst 327 (1990), 143–145.
4. 4 R. E. Mickens, Difference equation models of differential equations, Math Comput Model 11 (1988), 528–530.
5. 5 R. E. Mickens, Nonstandard finite difference schemes for differential equations, J Difference Equations Appl 8 (2002), 823–847.
6. 6 R. E. Mickens, Applications of nonstandard finite differences, World Scientific, Singapore, 2000.
7. 7 R. E. Mickens, Nonstandard difference models of differential equations, World Scientific, Singapore, 1994.
8. 8 P. M. Jordan, 2004–2005, private communications (with R. E. Mickens).
9. 9 W. Kaplan, Ordinary differential equations, Addison‐Wesley, Reading, MA, 1958.
10. 10 P. M. Jordan, Finite‐amplitude acoustic traveling waves in a fluid that saturates a porous, Phys Lett A 355 (2006), 216–221.