Kernel perturbations for a class of second-kind convolution Volterra equations with non-negative kernels
- de Hoog, F.R.
- Anderssen, R.S.
DOIAbstract
AbstractWithin the class of second-kind Volterra equations, an important subclass is the second-kind convolution equations with non-negative kernels k, with ‖k‖1<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 equa...
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