General linear methods for Volterra integral equations

Journal of Computational and Applied Mathematics

Volumn 234, Issue 9, 2010, Pages 2768-2782

  Izzo, G ^a   Jackiewicz, Z ^b,c   Messina, E ^a   Vecchio, A ^d  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^b ARIZONA STATE UNIVERSITY   (United States)

^c AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Poland)

^d CNR   (Italy)

Author keywords

Convolution test equation; General linear methods; Linear stability analysis; Order conditions; Volterra integral equations

Indexed keywords

GENERAL LINEAR METHODS; ORDER CONDITIONS; TEST EQUATIONS; VOLTERRA INTEGRAL EQUATIONS;

INTEGRAL EQUATIONS; LINEAR STABILITY ANALYSIS; NUMERICAL ANALYSIS; NUMERICAL METHODS;

CONVOLUTION;

EID: 77955278435     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2010.01.023     Document Type: Conference Paper

References (16)

1. H. Brunner, and P. van der Houwen The Numerical Solution of Volterra Equations 1986 North-Holland Amsterdam
2. R.K. Miller Almost-periodic behavior of solutions of nonlinear Volterra system Quart. Appl. Math. 28 1971 553 570
3. J.A. Nohel, Qualitative behaviour of solutions of nonlinear Volterra integral equations, Stability Problems of Solutions of Differential Equations, (Proc. NATO Advanced Study Inst., Padua, 1965), Oderisi, Gubbio, Italy, 1966, pp. 177210.
4. J.C. Butcher The Numerical Analysis of Ordinary Differential Equations. RungeKutta and General Linear Methods 1987 John Wiley & Sons Chichester, New York
5. J.C. Butcher General linear methods Acta Numer. 15 2006 157 256
6. C. Zhang, and S. Vandewalle General linear methods for Volterra integro-differential equations with memory SIAM J. Sci. Comput. 27 2006 2010 2031
7. J.C. Butcher, P. Chartier, and Z. Jackiewicz Nordsieck representation of DIMSIMs Numer. Algorithms 16 1997 209 230
8. J.C. Butcher, P. Chartier, and Z. Jackiewicz Experiments with a variable-order type 1 DIMSIM code Numer. Algorithms 22 1999 237 261
9. M.R. Crisci, E. Russo, and A. Vecchio Block methods for second kind Volterra equations Ric. Mat. XLIV 1995 507 524
10. J.J.H. Miller On the location of zeros of certain classes of polynomials with applications to numerical analysis J. Inst. Math. Appl. 8 1971 397 406
11. A. Bellen, Z. Jackiewicz, R. Vermiglio, and M. Zennaro Stability analysis of RungeKutta methods for Volterra integral equations of the second kind IMA J. Numer. Anal. 10 1990 103 118
12. H. Brunner, S.P. Nørsett, P.H.M. Wolkenfelt, On V 0 -stability of numerical methods for Volterra integral equations of the second kind, Report NW84/80, Mathematish Centrum, Amsterdam 1980.
13. A. Bellen, Z. Jackiewicz, R. Vermiglio, and M. Zennaro Natural continuous extensions of RungeKutta methods for Volterra integral equations of the second kind and their applications Math. Comput. 52 1989 49 63
14. J.D. Lambert Computational Methods in Ordinary Differential Equations 1973 John Wiley & Sons Chichester, New York
15. J. Schur ber Potenzreihen die im Innern des Einheitskreises beschrnkt sind J. Reine Angew. Math. 147 1916 205 232
16. Z. Jackiewicz General Linear Methods for Ordinary Differential Equations 2009 John Wiley & Sons