Convergence of a block-by-block method for nonlinear Volterra integro-differential equations
HTML articles powered by AMS MathViewer
- by Athena Makroglou PDF
- Math. Comp. 35 (1980), 783-796 Request permission
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
- Owe Axelsson, A class of $A$-stable methods, Nordisk Tidskr. Informationsbehandling (BIT) 9 (1969), 185–199. MR 255059, DOI 10.1007/bf01946812 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.
- H. Brunner and J. D. Lambert, Stability of numerical methods for Volterra integro-differential equations, Computing (Arch. Elektron. Rechnen) 12 (1974), no. 1, 75–89 (English, with German summary). MR 418490, DOI 10.1007/bf02239501
- Philip J. Davis and Philip Rabinowitz, Numerical integration, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1967. MR 0211604
- J. T. Day, A Runge-Kutta method for the numerical solution of the Goursat problem in hyperbolic partial differential equations, Comput. J. 9 (1966), 81–83. MR 192665, DOI 10.1093/comjnl/9.1.81
- Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons, Inc., New York-London, 1962. MR 0135729
- Peter Linz, Linear multistep methods for Volterra integro-differential equations, J. Assoc. Comput. Mach. 16 (1969), 295–301. MR 239786, DOI 10.1145/321510.321521 A. MAKROGLOU, Numerical Solution of Volterra Integro-Differential Equations, Ph. D. thesis, Univ. of Manchester, U. K., Feb. 1977.
- William L. Mocarsky, Convergence of step-by-step methods for non-linear integro-differential equations, J. Inst. Math. Appl. 8 (1971), 235–239. MR 287734
- Kenneth W. Neves, Automatic integration of functional differential equations: an approach, ACM Trans. Math. Software 1 (1975), no. 4, 357–368. MR 386313, DOI 10.1145/355656.355661
- Lucio Tavernini, One-step methods for the numerical solution of Volterra functional differential equations, SIAM J. Numer. Anal. 8 (1971), 786–795. MR 295617, DOI 10.1137/0708072 R. WEISS, Numerical Procedures for Volterra Integral Equations, Ph. D. thesis, Computer Centre, Australian National University, Canberra, 1972.
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Math. Comp. 35 (1980), 783-796
- MSC: Primary 65R20
- DOI: https://doi.org/10.1090/S0025-5718-1980-0572856-9
- MathSciNet review: 572856