Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Convergence of a block-by-block method for nonlinear Volterra integro-differential equations


Author: Athena Makroglou
Journal: Math. Comp. 35 (1980), 783-796
MSC: Primary 65R20
DOI: https://doi.org/10.1090/S0025-5718-1980-0572856-9
MathSciNet review: 572856
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The theory of a block-by-block method for solving Volterra integral equations is extended to nonsingular Volterra integro-differential equations. Convergence is proved and a rate of convergence is found. The convergence results obtained are analogous to those obtained by Weiss [12] for Volterra integral equations. Several numerical examples are included.


References [Enhancements On Off] (What's this?)

  • [1] O. AXELSON, "A class of A-stable methods," BIT, v. 9, 1969, pp. 185-199. MR 0255059 (40:8266)
  • [2] C. T. H. BAKER, A. MAKROGLOU & E. SHORT, Stability Regions for Volterra Integro-Differential Equations, Numerical Analysis Report #22, Dept. of Mathematics, Univ. of Manchester, U. K., September 1977.
  • [3] H. BRUNNER & J. D. LAMBERT, "Stability of numerical methods for Volterra integro-differential equations," Computing, v. 12, 1974, pp. 75-89. MR 0418490 (54:6529)
  • [4] PH. J. DAVIS & PH. RABINOWITZ, Numerical Integration, Blaisdell, Waltham, Mass., 1967. MR 0211604 (35:2482)
  • [5] J. T. DAY, "Note on the numerical solution of integro-differential equations," Comput. J., v. 9, 1967, pp. 394-395. MR 0192665 (33:890)
  • [6] P. HENRICI, Discrete Variable Methods in Ordinary Differential Equations, Wiley, New York, 1962. MR 0135729 (24:B1772)
  • [7] P. LINZ, "Linear multistep methods for Volterra integro-differential equations," J. Assoc. Comput. Mach., v. 16, 1969, p. 295. MR 0239786 (39:1143)
  • [8] A. MAKROGLOU, Numerical Solution of Volterra Integro-Differential Equations, Ph. D. thesis, Univ. of Manchester, U. K., Feb. 1977.
  • [9] W. L. MOCARSKY, "Convergence of step-by-step methods for non-linear integro-differential equations," J. Inst. Math. Appl., v. 8, 1971, p. 235. MR 0287734 (44:4937)
  • [10] K. W. NEVES, "Automatic integration of functional differential equations: an approach," ACM Trans. Math. Software, v. 1, 1975, pp. 357-368. MR 0386313 (52:7171)
  • [11] L. TAVERNINI, "One-step methods for Volterra functional differential equations," SIAM J. Numer. Anal., v. 8, 1971, pp. 766-795. MR 0295617 (45:4683)
  • [12] R. WEISS, Numerical Procedures for Volterra Integral Equations, Ph. D. thesis, Computer Centre, Australian National University, Canberra, 1972.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65R20

Retrieve articles in all journals with MSC: 65R20


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1980-0572856-9
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society