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Volumn 25, Issue 4, 2003, Pages 1273-1292

Solving degenerate reaction-diffusion equations via variable step Peaceman-Rachford splitting

Author keywords

Degeneracy; Linear stabilities; Monotonicity; Nonlinear reaction diffusion equations; Quenching singularity; Semidis cretization; Splitting; Time adaptation

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; DIFFUSION; PROBLEM SOLVING; QUENCHING;

EID: 4043160540     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827501380691     Document Type: Article
Times cited : (45)

References (32)
  • 1
    • 0002633639 scopus 로고
    • The quenching problem for nonlinear parabolic differential equations
    • Ordinary and Partial Differential Equations, Springer-Verlag, New York, Berlin
    • A. ACKER AND W. WALTER, The quenching problem for nonlinear parabolic differential equations, in Ordinary and Partial Differential Equations, Lecture Notes in Math. 564, Springer-Verlag, New York, Berlin, 1976, pp. 1-12.
    • (1976) Lecture Notes in Math. , vol.564 , pp. 1-12
    • Acker, A.1    Walter, W.2
  • 2
    • 0002419643 scopus 로고
    • Remarks on quenching
    • A. ACKER AND B. KAWOHL, Remarks on quenching, Nonlinear Anal., 13 (1989), pp. 53-61.
    • (1989) Nonlinear Anal. , vol.13 , pp. 53-61
    • Acker, A.1    Kawohl, B.2
  • 4
    • 0028443125 scopus 로고
    • Algorithm 731: A moving-grid interface for systems of one-dimensional time-dependent partial differential equations
    • J. G. BLOM AND P. A. ZEGELING, Algorithm 731: A moving-grid interface for systems of one-dimensional time-dependent partial differential equations, ACM Trans. Math. Software, 20 (1994), pp. 194-214.
    • (1994) ACM Trans. Math. Software , vol.20 , pp. 194-214
    • Blom, J.G.1    Zegeling, P.A.2
  • 5
    • 0005688324 scopus 로고    scopus 로고
    • A moving mesh method in multiblock domains with application to a combustion problem
    • W. CAO, W. HUANG, AND R. D. RUSSELL, A moving mesh method in multiblock domains with application to a combustion problem, Numer. Methods Partial Differential Equations, 15 (1999), pp. 449-467.
    • (1999) Numer. Methods Partial Differential Equations , vol.15 , pp. 449-467
    • Cao, W.1    Huang, W.2    Russell, R.D.3
  • 6
    • 0033294022 scopus 로고    scopus 로고
    • A study of monitor functions for two-dimensional adaptive mesh generation
    • W. CAO, W. HUANG, AND R. D. RUSSELL, A study of monitor functions for two-dimensional adaptive mesh generation, SIAM J. Sci. Comput., 20 (1999), pp. 1978-1994.
    • (1999) SIAM J. Sci. Comput. , vol.20 , pp. 1978-1994
    • Cao, W.1    Huang, W.2    Russell, R.D.3
  • 7
    • 0008064236 scopus 로고
    • Computation of the critical domain for quenching in an elliptic plate
    • C. Y. CHAN, Computation of the critical domain for quenching in an elliptic plate, Neural Parallel Sci. Comput. 1 (1993), pp. 153-162.
    • (1993) Neural Parallel Sci. Comput. , vol.1 , pp. 153-162
    • Chan, C.Y.1
  • 8
    • 0008015865 scopus 로고
    • Parabolic quenching for nonsmooth convex domains
    • C. Y. CHAN AND L. KE, Parabolic quenching for nonsmooth convex domains, J. Math. Anal. Appl., 186 (1994), pp. 52-65.
    • (1994) J. Math. Anal. Appl. , vol.186 , pp. 52-65
    • Chan, C.Y.1    Ke, L.2
  • 9
    • 0031103708 scopus 로고    scopus 로고
    • Channel flow of a viscous fluid in the boundary layer
    • C. Y. CHAN AND P. C. KONG, Channel flow of a viscous fluid in the boundary layer, Quart. J. Appl. Math., 55 (1997), pp. 51-56.
    • (1997) Quart. J. Appl. Math. , vol.55 , pp. 51-56
    • Chan, C.Y.1    Kong, P.C.2
  • 10
    • 38249041847 scopus 로고
    • On the stability of mesh equidistribution strategies for time-dependent partial differential equations
    • J. M. COYLE, J. E. FLAHERTY, AND R. LUDWIG, On the stability of mesh equidistribution strategies for time-dependent partial differential equations, J. Comput. Phys., 62 (1986), pp. 26-39.
    • (1986) J. Comput. Phys. , vol.62 , pp. 26-39
    • Coyle, J.M.1    Flaherty, J.E.2    Ludwig, R.3
  • 12
    • 0002259684 scopus 로고
    • Blow-up at the boundary for degenerate semilinear parabolic equations
    • M. S. FLOATER, Blow-up at the boundary for degenerate semilinear parabolic equations, Arch. Rational Mech. Anal., 114 (1991), pp. 57-77.
    • (1991) Arch. Rational Mech. Anal. , vol.114 , pp. 57-77
    • Floater, M.S.1
  • 13
    • 0001367417 scopus 로고
    • A numerical study of three moving-grid methods for one-dimensional partial differential equations which are based on the method of lines
    • 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. Comput. Phys., 89 (1990), pp. 349-388.
    • (1990) J. Comput. Phys. , vol.89 , pp. 349-388
    • Furzeland, R.M.1    Verwer, J.G.2    Zegeling, P.A.3
  • 14
    • 0041184489 scopus 로고    scopus 로고
    • Nth-order operator splitting schemes and nonreversible systems
    • D. GOLDMAN AND T. J. KAPER, Nth-order operator splitting schemes and nonreversible systems, SIAM J. Numer. Anal., 33 (1996), pp. 349-367.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 349-367
    • Goldman, D.1    Kaper, T.J.2
  • 16
    • 0345501255 scopus 로고
    • A hopscotch method for the Korteweg-de Vries equation
    • I. S. GREIG AND J. LL. MORRIS, A hopscotch method for the Korteweg-de Vries equation, J. Comput. Phys., 20 (1976), pp. 64-80.
    • (1976) J. Comput. Phys. , vol.20 , pp. 64-80
    • Greig, I.S.1    Morris, J.L.L.2
  • 19
    • 0008449934 scopus 로고
    • An adaptive Rothe method for nonlinear reaction-diffusion systems
    • J. LANG AND A. WALTER, An adaptive Rothe method for nonlinear reaction-diffusion systems, Appl. Numer. Math., 13 (1993), pp. 135-146.
    • (1993) Appl. Numer. Math. , vol.13 , pp. 135-146
    • Lang, J.1    Walter, A.2
  • 20
    • 0000576069 scopus 로고
    • Quenching, nonquenching, and beyond quenching for solutions of some parabolic equations
    • H. A. LEVINE, Quenching, nonquenching, and beyond quenching for solutions of some parabolic equations, Ann. Math. Pure. Appl., 4 (1989), pp. 243-260.
    • (1989) Ann. Math. Pure. Appl. , vol.4 , pp. 243-260
    • Levine, H.A.1
  • 22
    • 0018323228 scopus 로고
    • Channel flow with temperature-dependent viscosity and internal viscous dissipation
    • H. OCKENDON, Channel flow with temperature-dependent viscosity and internal viscous dissipation, J. Fluid Mech., 93 (1979), pp. 737-746.
    • (1979) J. Fluid Mech. , vol.93 , pp. 737-746
    • Ockendon, H.1
  • 23
    • 0002058827 scopus 로고
    • The numerical solution of parabolic and elliptic differential equations
    • D. W. PEACEMAN AND H. H. RACHFORD, JR., The numerical solution of parabolic and elliptic differential equations, J. Soc. Indust. Appl. Math., 3 (1955), pp. 28-41.
    • (1955) J. Soc. Indust. Appl. Math. , vol.3 , pp. 28-41
    • Peaceman, D.W.1    Rachford Jr., H.H.2
  • 24
    • 0000439427 scopus 로고
    • Finite element solution of diffusion problems with irregular data
    • R. RONNACHER, Finite element solution of diffusion problems with irregular data, Numer. Math., 43 (1984), pp. 309-327.
    • (1984) Numer. Math. , vol.43 , pp. 309-327
    • Ronnacher, R.1
  • 25
    • 0000631841 scopus 로고    scopus 로고
    • Stability of the Peaceman-rachford approximation
    • M. SCHATZMAN, Stability of the Peaceman-Rachford approximation, J. Funct. Anal., 162 (1999), pp. 219-255.
    • (1999) J. Funct. Anal. , vol.162 , pp. 219-255
    • Schatzman, M.1
  • 26
    • 0013403652 scopus 로고
    • Solving linear partial differential equations by exponential splitting
    • Q. SHENG, Solving linear partial differential equations by exponential splitting, IMA J. Numer. Anal., 9 (1989), pp. 199-212.
    • (1989) IMA J. Numer. Anal. , vol.9 , pp. 199-212
    • Sheng, Q.1
  • 28
    • 4043181254 scopus 로고    scopus 로고
    • A monotonically convergent adaptive method for nonlinear combustion problems
    • Integral Methods in Science and Engineering, Chapman & Hall/CRC, London, New York
    • Q. SHENG, A monotonically convergent adaptive method for nonlinear combustion problems, in Integral Methods in Science and Engineering, Res. Notes Math. 418, Chapman & Hall/CRC, London, New York, 2000, pp. 310-315.
    • (2000) Res. Notes Math. , vol.418 , pp. 310-315
    • Sheng, Q.1
  • 29
    • 0034209970 scopus 로고    scopus 로고
    • An adaptive grid method for degenerate semilinear quenching problems
    • Q. SHENG AND H. CHENG, An adaptive grid method for degenerate semilinear quenching problems, Comput. Math. Appl., 39 (2000), pp. 57-71.
    • (2000) Comput. Math. Appl. , vol.39 , pp. 57-71
    • Sheng, Q.1    Cheng, H.2
  • 30
    • 84894674651 scopus 로고    scopus 로고
    • Linearly implicit adaptive schemes for singular reaction-diffusion equations
    • A. Vande Wouwer, Ph. Saucez, and W. E. Schiesser, eds., Chapman & Hall/CRC, London, New York
    • Q. SHENG AND A. KHALIQ, Linearly implicit adaptive schemes for singular reaction-diffusion equations, in Adaptive Method of Lines, A. Vande Wouwer, Ph. Saucez, and W. E. Schiesser, eds., Chapman & Hall/CRC, London, New York, 2001, pp. 263-294.
    • (2001) Adaptive Method of Lines , pp. 263-294
    • Sheng, Q.1    Khaliq, A.2
  • 32
    • 0001057158 scopus 로고
    • Chaos-free numerical solutions of reaction-diffusion equations
    • E. H. TWIZELL, Y. WANG, AND W. G. PRICE, Chaos-free numerical solutions of reaction-diffusion equations, Proc. Roy. Soc. London Ser. A, 430 (1991), pp. 541-576.
    • (1991) Proc. Roy. Soc. London Ser. A , vol.430 , pp. 541-576
    • Twizell, E.H.1    Wang, Y.2    Price, W.G.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.