Numerical analysis of asymptotically convolution evolutionary integral equations

Abstract

Asymptotically convolution Volterra equations are characterized by kernel functions which exponentially decay to convolution ones. Their importance in the applications motivates a numerical analysis of the asymptotic behavior of the solution. Here the quasi-convolution nature of the kernel is exploited in order to investigate the stability of $\left(\rho ,\sigma \right)$ methods for general systems and in some particular cases.