메뉴 건너뛰기




Volumn 23, Issue 4, 1997, Pages 381-402

Mixed interpolation collocation methods for first and second order Volterra integro-differential equations with periodic solution

Author keywords

Collocation; First and second order; Mixed interpolation; Numerical solution; Periodic; Volterra integro differential equations

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; INTEGRODIFFERENTIAL EQUATIONS;

EID: 0031166382     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(96)00075-X     Document Type: Article
Times cited : (43)

References (26)
  • 1
    • 0018680479 scopus 로고
    • The collocation method for the numerical approximation of periodic solutions of functional differential equations
    • A. Bellen, The collocation method for the numerical approximation of periodic solutions of functional differential equations, Computing 23 (1979) 55-66.
    • (1979) Computing , vol.23 , pp. 55-66
    • Bellen, A.1
  • 2
    • 38249003451 scopus 로고
    • Numerical solution of Fredholm equations based on mixed interpolation
    • G. Vanden Berghe, P. Bocher and H. De Meyer, Numerical solution of Fredholm equations based on mixed interpolation, Appl. Numer. Math. 13 (1993) 15-22.
    • (1993) Appl. Numer. Math. , vol.13 , pp. 15-22
    • Vanden Berghe, G.1    Bocher, P.2    De Meyer, H.3
  • 3
    • 0001066401 scopus 로고
    • On a class of modified Newton-Cotes quadrature formulae based upon mixed-type interpolation
    • G. Vanden Berghe, H. De Meyer and J. Vanthournout, On a class of modified Newton-Cotes quadrature formulae based upon mixed-type interpolation, J. Comput. Appl. Math. 31 (1990) 331-349.
    • (1990) J. Comput. Appl. Math. , vol.31 , pp. 331-349
    • Vanden Berghe, G.1    De Meyer, H.2    Vanthournout, J.3
  • 4
    • 0005239563 scopus 로고
    • A modified Numerov integration method for second order periodic initial-value problems
    • G. Vanden Berghe, H. De Meyer and J. Vanthournout, A modified Numerov integration method for second order periodic initial-value problems, Internat. J. Comput. Math. 32 (1990) 233-242.
    • (1990) Internat. J. Comput. Math. , vol.32 , pp. 233-242
    • Vanden Berghe, G.1    De Meyer, H.2    Vanthournout, J.3
  • 5
    • 38149146147 scopus 로고
    • Numerical solution of Volterra equations based on mixed interpolation
    • P. Bocher, H. De Meyer and G. Vanden Berghe, Numerical solution of Volterra equations based on mixed interpolation, Comput. Math. Appl. 27 (1994) 1-11.
    • (1994) Comput. Math. Appl. , vol.27 , pp. 1-11
    • Bocher, P.1    De Meyer, H.2    Vanden Berghe, G.3
  • 6
    • 84968503497 scopus 로고
    • Collocation methods for nonlinear Volterra integro-differential equations with infinite delay
    • H. Brunner, Collocation methods for nonlinear Volterra integro-differential equations with infinite delay, Math. Comp. 53 (1989) 571-587.
    • (1989) Math. Comp. , vol.53 , pp. 571-587
    • Brunner, H.1
  • 7
    • 84968521907 scopus 로고
    • Implicit Runge-Kutta methods of optimal order for Volterra integro-differential equations
    • H. Brunner, Implicit Runge-Kutta methods of optimal order for Volterra integro-differential equations, Math. Comp. 41 (1984) 95-109.
    • (1984) Math. Comp. , vol.41 , pp. 95-109
    • Brunner, H.1
  • 8
    • 0023569364 scopus 로고
    • Implicit Runge-Kutta-Nyström methods for general second-order Volterra integro-differential equations
    • H. Brunner, Implicit Runge-Kutta-Nyström methods for general second-order Volterra integro-differential equations, Comput. Math. Appl. 14 (1987) 549-559.
    • (1987) Comput. Math. Appl. , vol.14 , pp. 549-559
    • Brunner, H.1
  • 9
    • 0003213842 scopus 로고
    • The Numerical Solution of Volterra Equations
    • North-Holland, Amsterdam
    • H. Brunner and P.J. van der Houwen, The Numerical Solution of Volterra Equations, CWI Monographs 3 (North-Holland, Amsterdam, 1986).
    • (1986) CWI Monographs , vol.3
    • Brunner, H.1    Van Der Houwen, P.J.2
  • 10
    • 0003196710 scopus 로고
    • Integrodifferential Equations and Delay Models in Population Dynamics
    • Springer, New York
    • J.M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics, Lecture Notes in Biomathematics 20 (Springer, New York, 1977).
    • (1977) Lecture Notes in Biomathematics , vol.20
    • Cushing, J.M.1
  • 12
    • 0000932450 scopus 로고
    • Unconditionally stable methods for second order differential equations
    • E. Hairer, Unconditionally stable methods for second order differential equations, Numer. Math. 32 (1979) 373-379.
    • (1979) Numer. Math. , vol.32 , pp. 373-379
    • Hairer, E.1
  • 13
    • 0016907498 scopus 로고
    • Existence of periodic solutions of a nerve equation
    • U. an den Heiden, Existence of periodic solutions of a nerve equation, Biol. Cybernetics 21 (1976) 37-39.
    • (1976) Biol. Cybernetics , vol.21 , pp. 37-39
    • An Den Heiden, U.1
  • 14
    • 0020939879 scopus 로고
    • High-order one-step P-stable methods for the numerical integration of periodic initial value problems
    • R.K. Jain, N.S. Kambo and R. Goel, High-order one-step P-stable methods for the numerical integration of periodic initial value problems, J. Comput. Appl. Math. 9 (1983) 361-367.
    • (1983) J. Comput. Appl. Math. , vol.9 , pp. 361-367
    • Jain, R.K.1    Kambo, N.S.2    Goel, R.3
  • 15
    • 0001194173 scopus 로고
    • Hopf bifurcation and stability of periodic solutions of differential-difference and integro-differential equations
    • N.D. Kazarinoff, Y.-H. Wan and P. van den Driessche, Hopf bifurcation and stability of periodic solutions of differential-difference and integro-differential equations, J. Inst. Math. Appl. 21 (1987) 461-477.
    • (1987) J. Inst. Math. Appl. , vol.21 , pp. 461-477
    • Kazarinoff, N.D.1    Wan, Y.-H.2    Van Den Driessche, P.3
  • 16
    • 0346927371 scopus 로고
    • On the numerical solution of Volterra integro-differential equations with periodic solutions; some preliminary results
    • University of Iowa
    • A. Makroglou and R.K. Miller, On the numerical solution of Volterra integro-differential equations with periodic solutions; some preliminary results, Presented at Midwest Conference on Differential Equations, University of Iowa (1991).
    • (1991) Midwest Conference on Differential Equations
    • Makroglou, A.1    Miller, R.K.2
  • 17
    • 0039541901 scopus 로고
    • On the numerical solution of Volterra integral equations with periodic solution; some preliminary results
    • Austin, TX
    • A. Makroglou and R.K. Miller, On the numerical solution of Volterra integral equations with periodic solution; some preliminary results, Presented at 7th Texas International Symposium on Approximation Theory, Austin, TX (1992).
    • (1992) 7th Texas International Symposium on Approximation Theory
    • Makroglou, A.1    Miller, R.K.2
  • 18
    • 0001249569 scopus 로고
    • Time-delay versus stability in population models with two and three trophic levels
    • R. May, Time-delay versus stability in population models with two and three trophic levels, Ecology 54 (1973) 315-325.
    • (1973) Ecology , vol.54 , pp. 315-325
    • May, R.1
  • 22
    • 0346927373 scopus 로고
    • Structure of solutions of unstable linear Volterra integrodifferential equations
    • R.K. Miller, Structure of solutions of unstable linear Volterra integrodifferential equations, J. Differential Equations 15 (1974) 129-157.
    • (1974) J. Differential Equations , vol.15 , pp. 129-157
    • Miller, R.K.1
  • 23
    • 0019057403 scopus 로고
    • On existence of periodic motions in nonlinear control systems with periodic inputs
    • R.K. Miller and A.N. Michel, On existence of periodic motions in nonlinear control systems with periodic inputs, SIAM J. Control Optim. 18 (1980) 585-598.
    • (1980) SIAM J. Control Optim. , vol.18 , pp. 585-598
    • Miller, R.K.1    Michel, A.N.2
  • 24
    • 0010967458 scopus 로고
    • The convergence of the spline collocation method for nonlinear differential equations
    • G. Vainikko, The convergence of the spline collocation method for nonlinear differential equations, Zh. Vychisl. Mat. i Mat. Fiz. 6 (1966) 35-42.
    • (1966) Zh. Vychisl. Mat. i Mat. Fiz. , vol.6 , pp. 35-42
    • Vainikko, G.1
  • 25
    • 44949279772 scopus 로고
    • Asymptotic expansion and geometric properties of the spline collocation periodic solution of an ODE system
    • L. Zhang, Asymptotic expansion and geometric properties of the spline collocation periodic solution of an ODE system, Appl. Math. Comput. 42 (1991) 209-221.
    • (1991) Appl. Math. Comput. , vol.42 , pp. 209-221
    • Zhang, L.1
  • 26
    • 0346927372 scopus 로고
    • Spline collocation approximation to periodic solutions of ordinary differential equations
    • L. Zhang, Spline collocation approximation to periodic solutions of ordinary differential equations, J. Comput. Math. 10 (1992) 147-154.
    • (1992) J. Comput. Math. , vol.10 , pp. 147-154
    • Zhang, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.