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Volumn 26, Issue 6, 2010, Pages 1556-1571

Computational methods for delay parabolic and time-fractional partial differential equations

Author keywords

? methods; Diffusion equations; Discretization; Fractional derivative order; Runke Kutta; Stability regions; Stiffness; Time lag

Indexed keywords

ASYMPTOTIC STABILITY; PARTIAL DIFFERENTIAL EQUATIONS; STIFFNESS;

EID: 78650109836     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20504     Document Type: Article
Times cited : (64)

References (24)
  • 1
    • 0018742204 scopus 로고
    • Spatial structures in predator-prey communities with hereditary effects and diffusion
    • D. S. Cohen, P. S. Hagan, and H. C. Simpson, Spatial structures in predator-prey communities with hereditary effects and diffusion, Math Biosci 44 (1979), 167-177.
    • (1979) Math Biosci , vol.44 , pp. 167-177
    • Cohen, D.S.1    Hagan, P.S.2    Simpson, H.C.3
  • 2
    • 0017140005 scopus 로고
    • Spatial structures in predator-prey comunities-A nonlinear time delay diffusional model
    • J. D. Murray, Spatial structures in predator-prey comunities-a nonlinear time delay diffusional model, Math Biosci 30 (1976), 73-85.
    • (1976) Math Biosci , vol.30 , pp. 73-85
    • Murray, J.D.1
  • 3
    • 0022180238 scopus 로고
    • Interaction of spatial diffusion and delays in models of genetic control by repression
    • S. N. Busenberg and J. M. Mahaffy, Interaction of spatial diffusion and delays in models of genetic control by repression, J Math Biol 22 (1985), 313-333.
    • (1985) J Math Biol , vol.22 , pp. 313-333
    • Busenberg, S.N.1    Mahaffy, J.M.2
  • 4
    • 0021171678 scopus 로고
    • Odels of genetic control by repression with time delays and spatial effects
    • J. M. Mahaffy and C. V. Pao, Models of genetic control by repression with time delays and spatial effects, J Math Biol 20 (1984), 39-57.
    • (1984) J Math Biol , vol.20 , pp. 39-57
    • Mahaffy, J.M.1    Pao, C.V.2
  • 5
    • 0042629252 scopus 로고
    • An abstract delay-differential equation modelling size dependent cell growth and division
    • M. Gyllenberg and H. J. A. Heijmans, An abstract delay-differential equation modelling size dependent cell growth and division, SIAM J Math Anal 18 (1987), 74-88.
    • (1987) SIAM J Math Anal , vol.18 , pp. 74-88
    • Gyllenberg, M.1    Heijmans, H.J.A.2
  • 6
    • 0041884410 scopus 로고
    • Multistability and boundary layer development in a transport equation with delayed arguments
    • A. O. Rey and M. C. Mackey, Multistability and boundary layer development in a transport equation with delayed arguments, Can Appl Math Quar 1 (1993), 1-21.
    • (1993) Can Appl Math Quar , vol.1 , pp. 1-21
    • Rey, A.O.1    Mackey, M.C.2
  • 7
    • 0016470398 scopus 로고
    • Optimal control of parabolic systems with boundary conditions involving time delays
    • P. K. Wang, Optimal control of parabolic systems with boundary conditions involving time delays, SIAM J Control 13 (1975), 274-293.
    • (1975) SIAM J Control , vol.13 , pp. 274-293
    • Wang, P.K.1
  • 12
    • 25144465409 scopus 로고    scopus 로고
    • Open issues in devising software for numerical solution of implicit delay differential equations
    • N. Guglielmi, Open issues in devising software for numerical solution of implicit delay differential equations, J Comput Appl Math 185 (2006), 261-277.
    • (2006) J Comput Appl Math , vol.185 , pp. 261-277
    • Guglielmi, N.1
  • 14
    • 0034891830 scopus 로고    scopus 로고
    • Implementing Radau IIA methods for stiff delay differential equations
    • N. Guglielmi and E. Hairer, Implementing Radau IIA methods for stiff delay differential equations, Computing 67 (2001), 1-12.
    • (2001) Computing , vol.67 , pp. 1-12
    • Guglielmi, N.1    Hairer, E.2
  • 17
    • 0035885643 scopus 로고    scopus 로고
    • The effects of temporal delays in a model for a food-limited, diffusing population
    • F. A. Davidson and S. A. Gourley, The effects of temporal delays in a model for a food-limited, diffusing population, J Math Anal Appl 261 (2001), 633-648.
    • (2001) J Math Anal Appl , vol.261 , pp. 633-648
    • Davidson, F.A.1    Gourley, S.A.2
  • 18
    • 33745885794 scopus 로고    scopus 로고
    • Nonlocality of reaction-diffusion equations included by delay: Biological modeling and nonlinear dynamics
    • S. A. Gourley, J.W.-H. So, and J. H.Wu, Nonlocality of reaction-diffusion equations included by delay: biological modeling and nonlinear dynamics, J Math Sci 124 (2004), 5119-5153.
    • (2004) J Math Sci , vol.124 , pp. 5119-5153
    • Gourley, S.A.1    So, J.W.-H.2    Wu, J.H.3
  • 19
    • 0031207489 scopus 로고    scopus 로고
    • Dynamics of constant and variable stepsize methods for a nonlinear population model with delay
    • T. K. Sardar and D. J. Higham, Dynamics of constant and variable stepsize methods for a nonlinear population model with delay, Appl Numer Math 24 (1997), 425-438.
    • (1997) Appl Numer Math , vol.24 , pp. 425-438
    • Sardar, T.K.1    Higham, D.J.2
  • 21
    • 34250257105 scopus 로고
    • Some aspects of the boundary locus method
    • J. M. Sanz-Serna, Some aspects of the boundary locus method, BIT 20 (1980), 97-101.
    • (1980) BIT , vol.20 , pp. 97-101
    • Sanz-Serna, J.M.1
  • 22
    • 0041792724 scopus 로고
    • On the computational solution of a class of functional differential equations
    • R. E. Bellman and K. L. Cooke, On the computational solution of a class of functional differential equations, J Math Anal Appl 12 (1965), 495-500.
    • (1965) J Math Anal Appl , vol.12 , pp. 495-500
    • Bellman, R.E.1    Cooke, K.L.2
  • 23
    • 0000714267 scopus 로고
    • The stability of the θ-methods in the numerical solution of delay differential equations
    • M. Liu and M. N. Spijker, The stability of the θ-methods in the numerical solution of delay differential equations, IMA J Numer Anal 10 (1990), 31-48.
    • (1990) IMA J Numer Anal , vol.10 , pp. 31-48
    • Liu, M.1    Spijker, M.N.2
  • 24
    • 38249024166 scopus 로고
    • Stability of numerical methods for delay differential equations
    • L. Torelli, Stability of numerical methods for delay differential equations, J Comput Appl Math 25 (1989), 15-26.
    • (1989) J Comput Appl Math , vol.25 , pp. 15-26
    • Torelli, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.