By Christopher T. H. Baker (auth.), Peter R. Turner (eds.)

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Extra resources for Topics in Numerical Analysis: Proceedings of the S.E.R.C. Summer School, Lancaster, July 19–August 21, 1981

Sample text

The insight obtained from such analysis is frequently obscured by the complexity of the theory. 6) are frequently appealed to. 6) might suggest. 6) is quite easy to settle in the light of the remarks which follow. g. 7) ~k+l = ~ ~k + ~k is frequently encountered. 6), M ~ M(%h). 7) should be familiar. 7). is required to be of class M. 7) is strictly stable if p(M) < I. 10) is a Schur polynomial, that is,it has its zeros in I~I

A. ) Solution methods for integral equations: tions, Plenum Press, New York (1979). W. Direct methods for the numerical solution of Volterra integral equations of the first kind. D. thesis, Univ. of Southampton (1976). W. & McKEE, S. Stability and convergence of multistep methods for linear Volterra equations of the first kind. SIAM. 269-292 (1976). de HOOG F. & WEISS, R. On the solution of Volterra integral equations of the first kind. Numer. Math. 2! pp. 22-32 (1973). J. Convergence and stability analysis of Runge-Kutta type methods for Volterra integral equations of the second kind.

Paper [21 ] gives as references earlier work related to his study. Eggermont'S The work of Cameron [18 ] is also, we believe, related. Brunner [communicated privately] has recently surveyed the literature on Volterra and Abel integral equations. As will be apparent from the emphasis here, and from consulting that survey, there remain a number of areas of interest for further work - particularly concerning Abel equations and Volterra equations of the first kind. By concentrating upon Volterra equations of the second kind we address a tractable problem in which the insight obtained moulds our expectations of what might be achieved for more difficult problems.

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