메뉴 건너뛰기




Volumn 23, Issue 3, 2007, Pages 672-691

Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition

Author keywords

Denominator functions; Nonstandard finite difference schemes; Numerical integration; Positive systems

Indexed keywords


EID: 34248181918     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20198     Document Type: Article
Times cited : (160)

References (17)
  • 1
    • 84985304745 scopus 로고
    • Exact solutions to a finite difference model of a nonlinear reaction‐advection equation: Implications for numerical analysis
    • 1 R. E. Mickens, Exact solutions to a finite difference model of a nonlinear reaction‐advection equation: Implications for numerical analysis, Numer Methods Partial Differential Eq 5 ( 1989), 313–325.
    • (1989) Numer Methods Partial Differential Eq , vol.5 , pp. 313-325
    • Mickens, R.E.1
  • 2
    • 0025599254 scopus 로고
    • Finite difference models of ordinary differential equations: Influence of denominator models
    • 2 R. E. Mickens and A. Smith, Finite difference models of ordinary differential equations: Influence of denominator models, J Franklin Institute 327 ( 1990), 143–145.
    • (1990) J Franklin Institute , vol.327 , pp. 143-145
    • Mickens, R.E.1    Smith, A.2
  • 3
    • 0003644445 scopus 로고
    • Nonstandard finite difference models of differential equations
    • 3 R. E. Mickens, Nonstandard finite difference models of differential equations, World Scientific, Singapore, 1994.
    • (1994)
    • Mickens, R.E.1
  • 4
    • 0000739387 scopus 로고    scopus 로고
    • Nonstandard finite difference schemes for reaction‐diffusion equations
    • 4 R. E. Mickens, Nonstandard finite difference schemes for reaction‐diffusion equations, Numer Methods Partial Differential Eq 15 ( 1999), 201–214.
    • (1999) Numer Methods Partial Differential Eq , vol.15 , pp. 201-214
    • Mickens, R.E.1
  • 5
    • 0003763818 scopus 로고    scopus 로고
    • Applications of nonstandard finite difference schemes
    • 5 R. E. Mickens, editor, Applications of nonstandard finite difference schemes, World Scientific, Singapore, 2000.
    • (2000)
  • 6
    • 85120588460 scopus 로고    scopus 로고
    • Advances in the application of nonstandard finite difference schemes
    • 6 R. E. Mickens, editor, Advances in the application of nonstandard finite difference schemes, World Scientific, Singapore, 2005.
    • (2005)
  • 7
    • 24144435933 scopus 로고    scopus 로고
    • On the use of nonstandard finite difference methods
    • 7 K. C. Patidar, On the use of nonstandard finite difference methods, J Differ Eq Appl 11 ( 2005), 735–758.
    • (2005) J Differ Eq Appl , vol.11 , pp. 735-758
    • Patidar, K.C.1
  • 8
    • 0003475470 scopus 로고
    • Mathematical biology
    • 8 J. D. Murray, Mathematical biology, Springer, Berlin, 1993.
    • (1993)
    • Murray, J.D.1
  • 9
    • 24144496812 scopus 로고    scopus 로고
    • Dynamic consistency: a fundamental principle for constructing NSFD schemes for differential equations
    • 9 R. E. Mickens, Dynamic consistency: a fundamental principle for constructing NSFD schemes for differential equations, J Differ Eq Appl 11 ( 2005), 645–653.
    • (2005) J Differ Eq Appl , vol.11 , pp. 645-653
    • Mickens, R.E.1
  • 10
    • 85120592512 scopus 로고    scopus 로고
    • Private communication from Timothy Reluga
    • 10 Private communication from Timothy Reluga, Yale University, New Haven, CT, 2005.
    • (2005)
  • 11
    • 0031189983 scopus 로고    scopus 로고
    • Numerical crisis found in the fixed step integration of a photoconductor model
    • 11 A. Serfaty de Markus, Numerical crisis found in the fixed step integration of a photoconductor model, Phys Rev E56 ( 1997), 88–93.
    • (1997) Phys Rev , vol.E56 , pp. 88-93
    • Serfaty de Markus, A.1
  • 12
    • 0032691079 scopus 로고    scopus 로고
    • Suppression of numerically induced chaos with nonstandard finite difference schemes
    • 12 A. Serfaty de Markus and R. E. Mickens, Suppression of numerically induced chaos with nonstandard finite difference schemes, J Comput Appl Math 106 ( 1999), 317–324.
    • (1999) J Comput Appl Math , vol.106 , pp. 317-324
    • Serfaty de Markus, A.1    Mickens, R.E.2
  • 13
    • 0003956985 scopus 로고    scopus 로고
    • Nonlinear partial differential equations
    • 13 L. Debnath, Nonlinear partial differential equations, Birkhäuser, Boston, 1997.
    • (1997)
    • Debnath, L.1
  • 14
    • 0026136722 scopus 로고
    • Analysis of a new finite‐difference scheme for the linear advection‐diffusion equation
    • 14 R. E. Mickens, Analysis of a new finite‐difference scheme for the linear advection‐diffusion equation, J Sound Vibration 146 ( 1991), 342–344.
    • (1991) J Sound Vibration , vol.146 , pp. 342-344
    • Mickens, R.E.1
  • 15
    • 0004131280 scopus 로고
    • Finite‐difference equations and simulations
    • 15 F. B. Hildebrand, Finite‐difference equations and simulations, Prentice‐Hall, Englewood Cliffs, NJ, 1968.
    • (1968)
    • Hildebrand, F.B.1
  • 16
    • 85093102251 scopus 로고    scopus 로고
    • Influence of spatial discretizations on nonstandard finite difference schemes for nonlinear PDE's
    • 16 R. E. Mickens, Influence of spatial discretizations on nonstandard finite difference schemes for nonlinear PDE's, Int J Appl Sci Comput 6 ( 1999), 89–95.
    • (1999) Int J Appl Sci Comput , vol.6 , pp. 89-95
    • Mickens, R.E.1
  • 17
    • 0004046327 scopus 로고
    • Difference equations: theory and applications
    • 17 R. E. Mickens, Difference equations: theory and applications, Chapman and Hall, New York, 1990.
    • (1990)
    • Mickens, R.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.