This paper studies the iterative learning control (ILC) for a class of second-order nonlinear hyperbolic impulsive partial differential systems. Firstly, to follow discontinuous desired output, P-type law is adopted, and sufficient conditions convergence tracking error established under identified initial state value. The rigorous analysis also given using Gronwall inequality. Secondly, output ...

the aim of the present paper is the investigation of some problems which can be reduced to thegoursat problem for a third order equation. some results and theorems are given concerning the existence anduniqunce for solving the suggested problem.

In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...

The first-order system LL* (FOSLL*) approach for general second-order elliptic partial differential equations was proposed and analyzed in [Z. Cai et al., SIAM J. Numer. Anal., 39 (2001), pp. 1418–1445], in order to retain the full efficiency of the L2 norm first-order system leastsquares (FOSLS) approach while exhibiting the generality of the inverse-norm FOSLS approach. The FOSLL* approach of...

analysis of iterative substructuring algorithms for elliptic problems in three dimensions. Least-squares mixed-nite elements for second-order elliptic problems. A least-squares approach based on a discrete minus one inner product for rst order systems. Technical report, Brookhaven National Laboratory, 1994. 4] J. H. Bramble and J. E. Pasciak. Least-squares methods for Stokes equations based on ...