A compound adaptive approach to degenerate nonlinear quenching problems

Numerical Methods for Partial Differential Equations

Volumn 15, Issue 1, 1999, Pages 29-47

  Sheng, Q ^a   Khaliq, A Q M ^b  

^a UNIVERSITY OF LOUISIANA AT LAFAYETTE   (United States)

^b WESTERN ILLINOIS UNIVERSITY   (United States)

Author keywords

Adaptive method; Finite difference scheme; Nonlinear partial differential equations; Quenching and combustion processes; Semidiscretization

Indexed keywords

EID: 0002801162     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2426(199901)15:1<29::AID-NUM2>3.0.CO;2-L     Document Type: Article

References (24)

1. M. C. Branch, M.W. Beckstead, T. A. Litzinger, M. D. Smooke, and V. H. Yang, "Nonsteady combustion mechanisms of advanced solid propellants," Annual Technical Report, 94-05, Center for Combustion and Environmental Research, University of Colorado, Boulder, CO (1994).
2. A. Ghafourian, C. Huyn, P. Johnson, S. Hevert, H. Dindi, S. Mahalingam, and J. W. Faily, "Liquid rocket combustion instability," Research Report, 90-02, Center for Combustion and Environmental Research, University of Colorado, Boulder, CO (1990).
3. W. Govaerts, "Seeking for reference on combustion problems," Numer. Anal. Digest 17, 5 (1997).
4. xx + 1/(1 - u)," Publ. Res. Inst. Math. Sci. 10, 729-736 (1975).
5. A. Acker and W. Walter, "The quenching problem for nonlinear parabolic differential equations," Lecture Notes in Math. 564, Springer-Verlag, New York, 1-12 (1976).
6. W. Walter, "Parabolic differential equations with a singular nonlinear term," Funkcial Ekvac. 19, 271-277 (1976).
7. C. S. Chen, "The method of fundamental solutions for nonlinear thermal explosions," Comm. Numer. Methods Engrg. 11, 675-681 (1995).
8. J. W. Mooney, "A numerical method for accurate critical length estimation in singular quenching problems," WSSIAA 4, 505-516 (1995).
9. C. Y. Chan, "Computation of the critical domain for quenching in an elliptic plate," Neural Parallel Sci. Comput. 1, 153-162 (1992).
10. C. Y. Chan, "Recent advances in quenching phenomena," Proc. Dynamic Systems & Appl. 2, 107-114 (1996).
11. C. Y. Chan and C. S. Chen, "A numerical method for semilinear singular parabolic mixed boundary-value problems," Quart. Appl. Math. 47, 45-57 (1989).
12. C. Y. Chan and C. S. Chen, "Method of fundamental solutions for multi-dimensional quenching problems," Research Report (1997).
13. Y. Tourigny and J. M. Sanz-Serna, "The numerical study of blow-up with application to a nonlinear Schrödinger equation," J. Comp. Phys. 102, 407-416 (1992).
14. D. A. Voss and A. Q. M. Khaliq, "Parallel LOD methods for second order time dependent PDEs," Computers Math. Applic. 30, 25-35 (1995).
15. A. Q. M. Khaliq, E. H. Twizell, and D. A. Voss, "On parallel algorithms for semidiscretized parabolic partial differential equations based on subdiagonal padé approximations," Num. Math, for Partial Diff. Eqs. 9, 107-116 (1993).
16. J. W. Mooney, "An implicit algorithm for iterating to quenching times in degenerate nonlinear parabolic problems," Dynamic Sys. Appl. 5, 539-551 (1996).
17. J. Lang, "Two-dimensional fully adaptive solutions of reaction-diffusion equations," Appl. Numer. Math. 18, 223-240 (1995).
18. J. Lang and A. Walter, "An adaptive Rothe method for nonlinear reaction-diffusion systems," Appl. Numer. Math. 13, 135-146 (1993).
19. t at quenching," Proc. Amer. Math. Soc. 106, 1049-1056 (1989).
20. H. A. Levine, "Quenching, nonquenching, and beyond quenching for solutions of some parabolic equations," Ann. Mat. Pure. Appl. 4, 243-260 (1989).
21. P. Henrici, Discrete Variable Methods in Ordinary Differential Equations, John Wiley & Sons, New York, 1962.
22. R. M. Furzeland, J. G. Verwer, and P. A. Zegeling, "A numerical study of three moving-grid methods for one-dimensional partial differential equations which are based on the method of lines," J. Comp. Physics 89, 349-388 (1990).
23. S. Filippas and J. S. Guo, "Quenching profiles for one-dimensional semilinear heat equations," Quart. Appl. Math. 51, 713-729 (1993).
24. E. S. Fraga and J. L. Morris, "An adaptive mesh refinement method for nonlinear dispersive wave equations," J. Comp. Physics 101, 94-103 (1992).