Parameter estimation for a Volterra integro-differential equation (Q1189148)

The problem of parameter identification in a Volterra integro- differential system with a weakly singular kernel of the form \(\omega'(t)=M\omega(t)+\int^ t_{-\infty}K(t-s,q)\omega(s)ds+F(t)\), \(t\geq 0\), \(\omega(0)=\mu\), \(\omega(s)=\varphi(s)\), \(s<0\), where \(M\) is an \(n\times n\) constant matrix, \(\mu\in R^ n\), \(\varphi\in L^ 1(- \infty,0;R^ n)\) and \(K(\cdot,q)\) is an \(n\times n\) singular kernel depending on a parameter \(q=(\alpha,\beta)\in R^ 2\) with \(0\leq \alpha<1\) and \(\beta > 0\), is considered. A quasilinearization method is used to identify the damping parameter in the system. Besides parameter identification the authors discuss numerical techniques for solving weakly singular Volterra equations. They use a product integration method based on Simpson's rule.