A new error analysis for a cubic spline approximate solution of a class of Volterra integro-differential equations

Authors:
Joseph A. Guzek and Gene A. Kemper

Journal:
Math. Comp. **27** (1973), 563-570

MSC:
Primary 65R05

DOI:
https://doi.org/10.1090/S0025-5718-1973-0337044-6

MathSciNet review:
0337044

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper a third-order numerical method is considered which utilizes a twice continuously differentiable third degree spline to approximate the solution of

*a*,

*b*]. The error analysis uses a technique usually associated with linear multistep methods.

**[1]**R. C. Buck,*Advanced Calculus*, 2nd ed., McGraw-Hill, New York, 1965. MR**42**#431.**[2]**J. A. Guzek & G. A. Kemper,*A Cubic Spline Approximate Solution of a Class of Integro-Differential Equations*, Proc. Conf. Numerical Mathematics, University of Manitoba, October 1971.**[3]**P. Henrici,*Discrete Variable Methods in Ordinary Differential Equations*, Wiley, New York, 1962. MR**24**#B1772. MR**0135729 (24:B1772)****[4]**H.-S. Hung,*Application of Linear Spline Functions to the Numerical Solution of Volterra Integral Equations of the Second Kind*, University of Wisconsin Comput. Sci. Tech. Rep. No. 27, 1968.**[5]**H.-S. Hung,*The Numerical Solution of Differential and Integral Equations by Spline Functions*, Math. Res. Center Tech. Rep. No. 1053, Mathematics Research Center, University of Wisconsin, Madison, Wis., 1970.**[6]**G. A. Kemper, "Linear multistep methods for a class of functional differential equations,"*Numer. Math.*, Band 19, 1972, pp. 361-372. MR**0317561 (47:6108)****[7]**P. Linz, "Linear multistep methods for Volterra integro-differential equations,"*J. Assoc. Comput. Mach.*, v. 16, 1969, pp. 295-301. MR**39**#1143. MR**0239786 (39:1143)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1973-0337044-6

Keywords:
Volterra integro-differential equations,
spline approximation

Article copyright:
© Copyright 1973
American Mathematical Society