메뉴 건너뛰기




Volumn 10, Issue 1, 1990, Pages 31-48

The stability of the θ-methods in the numerical solution of delay differential equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0000714267     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/10.1.31     Document Type: Article
Times cited : (109)

References (16)
  • 1
    • 0021374208 scopus 로고
    • Stability properties of numerical methods for solving delay differential equations
    • Al-Mutib, A. N. 1984 Stability properties of numerical methods for solving delay differential equations. J. Comput. Appl. Math. 10, 71-79.
    • (1984) J. Comput. Appl. Math , vol.10 , pp. 71-79
    • Al-Mutib, A.N.1
  • 2
    • 0016463497 scopus 로고
    • Special stability problems for functional differential equations
    • Barwell, V. K. 1975 Special stability problems for functional differential equations. BIT IS, 130-135.
    • (1975) BIT IS , pp. 130-135
    • Barwell, V.K.1
  • 3
    • 84968587322 scopus 로고
    • Butcher, J. C. 1987 The numerical analysis of ordinary differential equations, Runge-Kutta and general linear methods. Chichester: John Wiley.
    • (1987) Chichester: John Wiley
    • Butcher, J.C.1
  • 4
    • 0007057928 scopus 로고
    • On the asymptotic stability of 0-methods for delay differential equations
    • Calvo, M., & Grande, T. 1988 On the asymptotic stability of 0-methods for delay differential equations. Numer. Math. 54, 257-269.
    • (1988) Numer. Math , vol.54 , pp. 257-269
    • Calvo, M.1    Grande, T.2
  • 5
    • 0016103004 scopus 로고
    • Highly stable multistep methods for retarded differential equations
    • Cryer, C. W. 1974 Highly stable multistep methods for retarded differential equations. SIAM. Numer. Anal. 11, 788-797.
    • (1974) SIAM. Numer. Anal , vol.11 , pp. 788-797
    • Cryer, C.W.1
  • 6
    • 0002945485 scopus 로고
    • Error analysis for a class of methods for stiff nonlinear initial value problems
    • Dahlquist, G. 1976 Error analysis for a class of methods for stiff nonlinear initial value problems. Lecture Notes in Mathematics 506, 60-72.
    • (1976) Lecture Notes in Mathematics , vol.506 , pp. 60-72
    • Dahlquist, G.1
  • 7
    • 0014496579 scopus 로고
    • Algorithms for classical stability problems
    • Duffin, R. T. 1969 Algorithms for classical stability problems. SIAM Review 11, 196-213.
    • (1969) SIAM Review , vol.11 , pp. 196-213
    • Duffin, R.T.1
  • 8
    • 0021376613 scopus 로고
    • Stability in linear multistep methods for pure delay equations
    • Houwen, P. J. Van der, & Sommelier, B. P. 1984 Stability in linear multistep methods for pure delay equations. J. Comp. Appl. Math. 10, 55-63.
    • (1984) J. Comp. Appl. Math , vol.10 , pp. 55-63
    • Van Der Houwen, P.J.1    Sommelier, B.P.2
  • 9
    • 0001044031 scopus 로고
    • Asymptotic stability analysis of 0-methods for functional differential equations
    • Jackiewicz, Z. 1984 Asymptotic stability analysis of 0-methods for functional differential equations. Numer. Math. 43, 389-396.
    • (1984) Numer. Math , vol.43 , pp. 389-396
    • Jackiewicz, Z.1
  • 10
    • 0000393697 scopus 로고
    • On the location of zeros of certain classes of polynomial with applications to numerical analysis
    • John, J., & Miller, J. H. 1971 On the location of zeros of certain classes of polynomial with applications to numerical analysis. J. Inst. Math. Appl. 8, 397-406.
    • (1971) J. Inst. Math. Appl , vol.8 , pp. 397-406
    • John, J.1    Miller, J.H.2
  • 11
    • 0022212912 scopus 로고
    • B-convergence of the implicit midpoint rule and the trapezoidal rule
    • Kraauevanoer, J. F. B. M. 1985 B-convergence of the implicit midpoint rule and the trapezoidal rule. BIT 25, 652-666.
    • (1985) BIT , vol.25 , pp. 652-666
    • Kraauevanoer, J.F.B.M.1
  • 13
    • 0040109369 scopus 로고
    • Contractivity in the numerical solution of initial value problems
    • Spuker, M. N. 1983 Contractivity in the numerical solution of initial value problems. Numer. Math. 42, 271-290.
    • (1983) Numer. Math , vol.42 , pp. 271-290
    • Spuker, M.N.1
  • 14
    • 0022016198 scopus 로고
    • The stability of difference formulas for delay differential equations
    • Watanabe, D. S., & Roth, M. G. 1985 The stability of difference formulas for delay differential equations. SIAM. Numer. Anal. 22, 132-145.
    • (1985) SIAM. Numer. Anal , vol.22 , pp. 132-145
    • Watanabe, D.S.1    Roth, M.G.2
  • 15
    • 0040944319 scopus 로고
    • On the P-stability of one-step collocation for delay differential equations
    • Zennaro, Marino 1985 On the P-stability of one-step collocation for delay differential equations. ISNM 74, 334-343.
    • (1985) ISNM , vol.74 , pp. 334-343
    • Zennaro, M.1
  • 16
    • 0000750163 scopus 로고
    • P-stability properties of Runge-Kutta methods for delay differential equations
    • Zennaro, Marino 1986 P-stability properties of Runge-Kutta methods for delay differential equations. Numer. Math. 49, 305-318.
    • (1986) Numer. Math , vol.49 , pp. 305-318
    • Zennaro, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.