메뉴 건너뛰기




Volumn 9, Issue 11, 2003, Pages 995-1006

Exact Solutions to a Finite-difference Model of a Nonlinear Reaction-advection Equation: Implications for Numerical Analysis

Author keywords

Difference equations; Differential equation; Finite difference model; Nonlinear reaetion advection equation

Indexed keywords


EID: 0141457696     PISSN: 10236198     EISSN: None     Source Type: Journal    
DOI: 10.1080/1023619031000146959     Document Type: Review
Times cited : (9)

References (19)
  • 2
    • 0021601406 scopus 로고
    • Aggregative efforts for a reaction-advection equation
    • R. Dal Passo and P. de Mottoni, Aggregative efforts for a reaction-advection equation, J. Math. Biol., 20 (1984), 103-112.
    • (1984) J. Math. Biol. , vol.20 , pp. 103-112
    • Dal Passo, R.1    De Mottoni, P.2
  • 5
    • 0004380661 scopus 로고
    • Focusing: A mechanism for instability of nonlinear finite difference equations
    • W. L. Briggs, A. C. Newell and T. Sarie, Focusing: a mechanism for instability of nonlinear finite difference equations, J. Comput. Phys., 51 (1983), 83-106.
    • (1983) J. Comput. Phys. , vol.51 , pp. 83-106
    • Briggs, W.L.1    Newell, A.C.2    Sarie, T.3
  • 6
    • 84985386829 scopus 로고
    • A numerical study of chaos in a reaction-diffusion equation
    • A. R. Mitchell and J. C. Bruch, Jr., A numerical study of chaos in a reaction-diffusion equation, Numer. Methods Partial Diff. Eq., 1 (1985), 13-23.
    • (1985) Numer. Methods Partial Diff. Eq. , vol.1 , pp. 13-23
    • Mitchell, A.R.1    Bruch J.C., Jr.2
  • 7
    • 84985373737 scopus 로고
    • Exact solutions to difference equation models of Burgers' equation
    • R. E. Mickens, Exact solutions to difference equation models of Burgers' equation, Numer. Methods Partial Diff. Eq., 2 (1986), 123-129.
    • (1986) Numer. Methods Partial Diff. Eq. , vol.2 , pp. 123-129
    • Mickens, R.E.1
  • 8
    • 77953616431 scopus 로고
    • Difference equation models of differential equations having zero local truncation errors
    • I. W. Knowles and R. T. Lewis, eds, North-Holland, Amsterdam
    • R. E. Mickens, Difference equation models of differential equations having zero local truncation errors, In: I. W. Knowles and R. T. Lewis, eds, Differential Equations, North-Holland, Amsterdam, 1984, pp. 445-449.
    • (1984) Differential Equations , pp. 445-449
    • Mickens, R.E.1
  • 10
    • 0000258580 scopus 로고
    • Differential and difference equations
    • R. B. Potts, Differential and difference equations, Am. Math. Monthly, 89 (1982), 402-407.
    • (1982) Am. Math. Monthly , vol.89 , pp. 402-407
    • Potts, R.B.1
  • 11
    • 0141653729 scopus 로고
    • Mathematical modeling of differential equations by difference equations
    • D. Lee, R. L. Steinberg and M. H. Schultz, eds, North-Holland, Amsterdam
    • R. E. Mickens, Mathematical modeling of differential equations by difference equations, In: D. Lee, R. L. Steinberg and M. H. Schultz, eds, Proceedings of the First IMAC Conference on Computational Acoustics, North-Holland, Amsterdam, 1987.
    • (1987) Proceedings of the First IMAC Conference on Computational Acoustics
    • Mickens, R.E.1
  • 15
    • 0001650860 scopus 로고
    • Chaos in numerical analysis of ordinary differential equations
    • M. Yamaguti and S. Ushiki, Chaos in numerical analysis of ordinary differential equations, Physica, 3D (1981), 618-626.
    • (1981) Physica , vol.3 D , pp. 618-626
    • Yamaguti, M.1    Ushiki, S.2
  • 16
    • 0141653727 scopus 로고
    • Runge-Kutta schemes and numerical instabilities: The logistic equation
    • I. Knowles and Y. Saito, eds, Springer-Verlag, Berlin
    • R. E. Mickens, Runge-Kutta schemes and numerical instabilities: the logistic equation, In: I. Knowles and Y. Saito, eds, Differential Equations and Mathematical Physics, Springer-Verlag, Berlin, 1987.
    • (1987) Differential Equations and Mathematical Physics
    • Mickens, R.E.1
  • 17
    • 0040115229 scopus 로고
    • Euler's finite difference scheme and chaos
    • M. Yamaguti and H. Matano, Euler's finite difference scheme and chaos, Proc. Japan Acad., 55 (1979), 78-80.
    • (1979) Proc. Japan Acad. , vol.55 , pp. 78-80
    • Yamaguti, M.1    Matano, H.2
  • 18
    • 0000644645 scopus 로고
    • Central difference scheme and chaos
    • S. Ushiki, Central difference scheme and chaos, Physica, 4D (1982), 407-424.
    • (1982) Physica , vol.4 D , pp. 407-424
    • Ushiki, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.