[Show abstract][Hide abstract] ABSTRACT: In this paper, we introduce efficient methods for the approximation of solutions to weakly singular Volterra integral equations of the second kind with highly oscillatory Bessel kernels. Based on the asymptotic analysis of the solution, we derive corresponding convergence rates in terms of the frequency for the Filon method, and for piecewise constant and linear collocation methods. We also present asymptotic schemes for large values of the frequency. These schemes possess the property that the numerical solutions become more accurate as the frequency increases.
[Show abstract][Hide abstract] ABSTRACT: In this paper, we consider an inverse problem for a linear time invariant dynamic system with noise. It is shown that after adjusting the system by shifting the eigenvalues of the system matrix, the disturbance of the system noise can be reduced and the input signal of certain types of the system can be recovered from the discrete observations of the system output.
International Journal of Control 02/2007; 62(6):1291-1317. · 1.14 Impact Factor
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