Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1708831 | Applied Mathematics Letters | 2012 | 4 Pages |
Abstract
Within the class of second-kind Volterra equations, an important subclass is the second-kind convolution equations with non-negative kernels k, with âkâ1<1, and positive forcing terms. Sharper results about the effect of kernel perturbations are obtained if attention is focussed on this subclass. In the standard perturbation and stability analysis for second-kind Volterra integral equations, it is the effect on the solution of perturbations in the forcing term and the stability of numerical methods for their solution that are examined. In applications, where only approximations for the kernel are available, such as arise in rheology, risk analysis, and renewal theory, the effect on the solution of perturbations in the kernel is equally important. In this paper, estimates are derived for this situation. The resolvent kernel framework is used to establish conditions such that, with respect to relative error perturbations in the kernel, the corresponding relative error perturbations in the solution are bounded. Defect renewal equations form a subset of the convolution Volterra integral equations examined.
Keywords
Related Topics
Physical Sciences and Engineering
Engineering
Computational Mechanics
Authors
F.R. de Hoog, R.S. Anderssen,