Pollution has become a very serious threat to our environment. Monitoring pollution is the rst step toward planning to save the environment. The use of dierential equations, monitoring pollution has become possible. In this paper, a Ritz-collocation method is introduced to solve non-linear oscillatory systems such as modelling the pollution of a system of lakes. The method is based upon Bernoul...

g. darbo [rend. sem. math. univ. padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. in this paper, we apply the darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.

this study develops and analyzes preconditioned krylov subspace methods to solve linear systemsarising from discretization of the time-independent space-fractional models. first, we apply shifted grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. then, we employee two preconditioned iterative methods, namely, the preconditioned gene...

Distributed live streaming has brought a lot of interest in the past few years. In the homogeneous case (all nodes having the same capacity), many algorithms have been proposed, which have been proven almost optimal or optimal. On the other hand, the performance of heterogeneous systems is not completely understood yet. In this paper, we investigate the impact of heterogeneity on the achievable...

This paper presents an exact method for solving logical loops in reliability analysis. The systems that include logical loops are usually described by simultaneous Boolean equations. First, present a basic rule of solving simultaneous Boolean equations. Next, show the analysis procedures for three-component system with external supports. Third, more detailed discussions are given for the establ...

In this paper, the ultraspherical operational matrices of derivatives are constructed. Based on these operational matrices, two numerical algorithms are presented and analyzed for obtaining new approximate spectral solutions of a class of linear and nonlinear Lane-Emden type singular initial value problems. The basic idea behind the suggested algorithms is basically built on transforming the eq...

Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation or transport phenomena, and heredity and competition in population dynamics. The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stabi...

in this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the fr´echet spaces. our aim is to provide a few generalization of tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of tych...