Product integration rules for volterra integral equations of the first kind

1987 ◽  
Vol 27 (2) ◽  
pp. 235-247 ◽  
Author(s):  
L. G. McAlevey
Keyword(s):  
Integral Equations ◽  
Volterra Integral Equations ◽  
Product Integration ◽  
Integration Rules

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

1987 ◽  
Vol 106 (3-4) ◽  
pp. 361-373 ◽  
Author(s):  
J. Norbury ◽  
A. M. Stuart
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
Volterra Integral Equations ◽  
Linear Case ◽  
Gronwall Inequality ◽  
Product Integration ◽  
Weakly Singular ◽  
Grönwall Inequality ◽  
Discrete Inequalities ◽  
Singular Kernels

SynopsisWe 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.

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