In this paper, a class of linear systems with multiple time delays is studied. The problem of exponential stability of time-delay systems has been investigated by using Lyapunov functional method. We will convert the system of multiple time delays into a single time delay system and show that if the old system is stable then the new one is so. Then we investigate the stability of converted new system, by using matrix decomposition and linear matrix inequality (LMI) technique. Some numerical examples are given to illustrate the efficiency of our method.

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The numerical method developed in the current paper is based on the moving least squares (MLS) method. To this end, the MLS approximation method has been used, and a program has been made which can solve the system of Volterra integral equations (VIEs) with any number of equations and unknown functions. And then the proposed method is implemented on the system of linear VIEs with variable coefficients. The numerical examples are given that show the acceptable accuracy and efficiency of the proposed scheme.

This paper addresses modified-meshless numerical schemes for dynamical systems with proportional delays. The proposed mesh reduction techniques are based on a redial-point interpolation and moving least-squares methods. An optimal influence domain radius is constructed utilizing nodal connectivity and node-depending integration background mesh. Optimal shape parameters are obtained by the use of properties of the delta Kronecker and the compactly supported weight function. Numerical results are provided to justify the accuracy and efficiency of the proposed schemes.

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