On the numerical solution of nonlinear systems of Volterra integro-differential equations with delay arguments

Computing (Vienna/New York)

Volumn 82, Issue 4, 2008, Pages 241-260

  Shakourifar, M ^a   Dehghan, M ^a  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Delay Volterra integro differential equations; Global convergence; Optimal order of superconvergence; Piecewise polynomial collocation

Indexed keywords

COMPUTER NETWORKS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); DYNAMICS; INTEGRAL EQUATIONS; INTEGRODIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; NUMERICAL METHODS;

DELAY VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS; GLOBAL CONVERGENCE; OPTIMAL ORDER OF SUPERCONVERGENCE; PIECEWISE POLYNOMIAL COLLOCATION; PREDATOR-PREY;

NONLINEAR EQUATIONS;

EID: 51349122661     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00607-008-0009-4     Document Type: Article

References (20)

1. Volterra V (1927) Variazioni e fluttuazioni del numero d'individui in specie animali conviventi. Memorie del R. Comitato talassografico italiano, Mem. CXXXI
2. Cushing JM (1977) Integrodifferential equations and delay models in population dynamics. Lecture notes in biomathematics, vol 20. Springer, Berlin
3. Volterra V (1939) The general equations of biological strife in the case of historical actions. Proc Edinburgh Math Soc 2: 4-10
4. Bocharov GA, Rihan FA (2000) Numerical modelling in biosciences using delay differential equations. J Comput Appl Math 125: 183-199
5. Gopalsamy K (1992) Stability and oscillation in delay differential equations of population dynamics. Kluwer, Boston
6. Kuang Y (1993) Delay differential equations with applications in population dynamic. Academic Press, San Diego, CA
7. Baker CTH, Ford NJ (1990) Asymptotic error expansions for linear multistep methods for a class of delay integro-differential equations. Bull Greek Math Soc 31: 5-10
8. Enright WH, Hu M (1997) Continuous Runge-Kutta methods for neutral Volterra integro-differential equations with delay. Appl Numer Math 24: 175-190
9. Brunner H (1988) The approximate solution of initial- value problems for general Volterra integro-differential equations. Computing 40: 125-137
10. Makroglou A (1983) A bloc-by-block method for the numerical solution of Volterra delay integro-differential equation. Computing 30: 49-62
11. Brunner H (1989) Collocation methods for nonlinear Volterra Integro-differential equations with infinite delay. Math Comp 53: 571-587
12. Brunner H (1994) The numerical solution of neutral Volterra integro-differential equations with delay arguments. Ann Numer Math 1: 309-322
13. Brunner H, Zhang W (1999) Primary discontinuities in solutions for delay integro-differential equations. Methods Appl Anal 6: 525-534
14. Baker CTH, Willé D (2000) On the propagation of derivative discontinuities in Volterra retarded integro-differential equations. N Z J Math 29: 103-113
15. Brunner H (1998) The use of splines in the numerical solution of Volterra integral and integro-differential equations. In: Dubuc S (ed) Splines and the theory of wavelets I, II, CRM Proceedings and Lecture Notes. American Mathematical Society, Providence, RI
16. Brunner H (1984) Implicit Runge-Kutta methods of optimal order for volterra integro-differential equations. Math Comp 42: 95-109
17. Atkinson KE (1989) Introduction to numerical analysis, 2nd edn. Wiley, New York
18. McKee S (1982) Generalized discrete Gronwall lemmas. Z Angew Math Mech 62: 429-434
19. Brunner H (2004) Collocation methods for Volterra integral and related functional equations. Cambridge University Press, Cambridge
20. Enright WH (2005) Tools for verification of approximate solutions to differential equations. In: Einarsson B(eds) Handbook for scientific computing. SIAM Press, Philadelphia, pp 109-119