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Published January 1987 | public
Journal Article

Volterra integral equations and a new Gronwall inequality (Part I: The linear case)

Abstract

We present a generalisation of the continuous Gronwall inequality and show its use in bounding solutions of discrete inequalities of a form that arise when analysing the convergence of product integration methods for Volterra integral equations. We then use these ideas to prove convergence of a numerical method which is effective in approximating Volterra integral equations of the second kind with weakly singular kernels.

Additional Information

© 1987 Royal Society of Edinburgh. MS received 8 July 1986. Revised MS received 11 February 1987. Published online: 14 November 2011. The second author is grateful to the Science and Engineering Research Council for financial support.

Additional details

Created:
August 19, 2023
Modified:
March 5, 2024