We develop and apply the product integration method to a large class of linear weakly singular Volterra systems. We show that under certain sufficient conditions this method converges. Numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.

In this paper, an algorithm based on the Drazin generalized conjugate residual (DGMRES) algorithm is proposed for computing the group-inverse solution of singular linear equations with index one. Numerical experiments show that the resulting group-inverse solution is reasonably accurate and its computation time is significantly less than that of group-inverse solution obtained by the DGMRES alg...

In this paper, we investigate a singular perturbation problem including a fourth order O.D.E. with general linear boundary conditions. Firstly, we obtain the necessary conditions of solution of O.D.E. by making use of fundamental solution, then by compatibility of these conditions with boundary conditions, we determine that, for given perturbation problem, whether boundary layer is formed or not.

The notion of balanced realizations for nonlinear state space model reduction problems was first introduced by Scherpen in 1993. Analogous to the linear case, the so called singular valuefunctions of a system describe the relative importance of each state component from an input-output point of view. In this paper it is shown that the procedure for nonlinear balancing has some interesting ambig...

parameterized by θ ∈ R . But we do not expect that the “sum” of two such solutions will again be a solution. However, the special class of soliton equations, the subject of this article, does have a form of nonlinear superposition. An n-soliton solution is a solution that is asymptotic to a nontrivial sum of n solitary waves ∑n i=1 fi(x− cit) as t → −∞ and to the sum of the same waves ∑n i=1 fi...

This paper presents a necessary and sufficient condition for discrete-time singular Markovian jump linear systems with defective statistics of modes transitions to be regular, causal, and stochastically stable. The static output-feedback stabilization problem for discrete-time singular Markovian jump linear system with defective statistics of modes transitions is studied. Furthermore, the defec...

Abstract : A new algorithm for noise filtering, based on non-linear processing of image in blocks, using singular value decomposition (SVD) is presented in this paper. Noise filtering is performed in the domain of singular values and singular vectors. A priori noise variance knowledge is not required, because a singular value-based noise variance estimation is performed in the first phase of th...

We present a general method for solving the non–linear differential equation of monotonically increasing steady–state radiation driven winds. We graphically identify all the singular points before transforming the momentum equation to a system of differential equations with all the gradients explicitly give. This permits a topological classification of all singular points and to calculate the m...

We consider the identi®cation of Hammerstein/non-linear feedback models by approximating internal non-linearities using piecewise linear static maps. The resulting method utilizes a point-slope parameterization that leads to a computationally tractable optimization problem. The computational appeal of this technique is derived from the fact that the method only requires a matrix inverse and sin...