On certain extrapolation methods for the numerical solution of integro-differential equations

Author:
S. H. Chang

Journal:
Math. Comp. **39** (1982), 165-171

MSC:
Primary 65R20

DOI:
https://doi.org/10.1090/S0025-5718-1982-0658220-4

MathSciNet review:
658220

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Abstract | References | Similar Articles | Additional Information

Abstract: Asymptotic error expansions have been obtained for certain numerical methods for linear Volterra integro-differential equations. These results permit the application of extrapolation procedures. Computational examples are presented.

**[1]**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)****[2]**J. T. Day, "Note on the numerical solution of integro-differential equations,"*Comput. J.*, v. 9, 1967, pp. 394-395. MR**0192665 (33:890)****[3]**A. Feldstein & J. R. Sopka, "Numerical methods for nonlinear Volterra integro-differential equations,"*SIAM J. Numer. Anal.*, v. 11, 1974, pp. 826-846. MR**0375816 (51:12006)****[4]**A. Goldfine, "Taylor series methods for the solution of Volterra integral and integro-differential equations,"*Math. Comp.*, v. 31, 1977, pp. 691-707. MR**0440970 (55:13838)****[5]**F. B. Hildebrand,*Introduction to Numerical Analysis*, 2nd ed., McGraw-Hill, New York, 1974. MR**0347033 (49:11753)****[6]**P. Linz, "Linear multistep methods for Volterra integro-differential equations,"*J. Assoc. Comput. Mach.*, v. 16, 1969, pp. 295-301. MR**0239786 (39:1143)****[7]**P. Linz, "A simple approximation method for solving Volterra integro-differential equations of the first kind,"*J. Inst. Math. Appl.*, J. 14, 1974, pp. 211-215. MR**0483593 (58:3585)****[8]**A. Makroglou, "Convergence of a block-by-block method for nonlinear Volterra integro-differential equations,"*Math. Comp.*, v. 35, 1980, pp. 783-796. MR**572856 (81g:65180)****[9]**S. McKee, "Cyclic multistep methods for solving Volterra integro-differential equations,"*SIAM J. Numer. Anal.*, v. 16, 1979, pp. 106-114. MR**518687 (80k:65105)****[10]**W. L. Mocarsky, "Convergence of step-by-step methods for non-linear integro-differential equations,"*J. Inst. Math. Appl.*, v. 8, 1971, pp. 235-239. MR**0287734 (44:4937)****[11]**M. A. Wolfe & G. M. Phillips, "Some methods for the solution of non-singular Volterra integro-differential equations,"*Comput. J.*, v. 11, 1968/69, pp. 334-336. MR**0235762 (38:4065)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1982-0658220-4

Article copyright:
© Copyright 1982
American Mathematical Society