Mathematical Sciences最新文献

In this paper, we propose an iterative scheme for a common fixed point of a countable family of quasi-nonexpansive mappings. The scheme is computationally less expensive, built on a geodesic averaging technique involving only selected elements. At each iteration, the scheme requires only geodesic segments and no further technical looping or optimizations. Under distinct mild conditions, we establish both (triangle)-convergence and strong convergence result for the proposed scheme to the required point, assuming existence. Notably, the considered mappings need not have compact images, among other relaxed conditions. Additionally, numerical experiments conducted show the robustness of the scheme. The results presented in this paper, not only enhances the existing related literature, but also offers valuable complements to previous studies.

A mathematical model is used to represent a physical system. To mimic closely to a real system, the mathematical model may present in functional differential equations. Most of the processes exhibit multiple time-varying delayed phenomena. This paper aims to develop a memory-less controller that achieves H(_infty) performance for disturbance rejection. The proposed technique for controller design ensures closed-loop stability of a chosen Lyapunov-Krasovskii functional (LKF). while, the integral functions derived from the LKF’s derivative are addressed through the utilization of free matrix inequality The development of stability condition is presented in linear matrix inequality. Based on the developed stability condition, the optimal controller gain is obtained after minimization of the H(_infty) performance. The proposed controller design technique is simulated to stabilize a diabetes system upon periodic glucose absorption as a disturbance function. Clearly, the controller is able to regulate insulin maintaining the blood glucose concentration to the healthy patient concentration upon introducing meal ingestion as periodic disturbances. Compare to an existing method, the proposed controller has lower peak in the rejecting the introducing disturbances.

Abstract

This paper proposes a sixth-order compact difference scheme of Poisson equation based on the sixth-order compact difference operator of the second derivative. The biggest difference between the proposed scheme and other sixth-order scheme is that the right hand contains second partial derivation of source term; this term makes the proposed scheme more accurate than other sixth-order schemes. The proposed scheme is combined with the multigrid method to solve two- and three-dimensional Poisson equations with Dirichlet boundary conditions. The result is compared with other sixth-order schemes in several numerical experiments. The numerical results show that the proposed scheme achieves the desired accuracy and has smaller errors than other schemes of the same order. Further, the multigrid method is higher efficient than traditional iterative method in accelerating the convergence.

Abstract

In this paper, we obtain some best proximity point results by introducing the concepts of proximal p-contractions of the first type and proximal p -contractions of the second type on partial metric spaces. Thus, some famous results in the literature such as the main result of Altun et al. (Acta Math Hung 162:393–402, 2020) and Basha (J Approx Theory 163(11):1772–1781, 2011) have been extended. Also, we provide some examples where our results are applicable and the results in Haghi et al. (Topol Appl 160:450–454, 2013) are not. Hence, our results are a real generalization of some results in metric spaces and partial metric spaces. Finally, we obtain sufficient conditions for the existence of the solution of nonlinear fractional differential equations via our results.

The inverse nodal problem for Sturm–Liouville operator with a constant delay has been investigated in the present paper. To do so, we have computed the nodal points and nodal lengths. Therefore, we have tried Chebyshev interpolation technique (CIT) to obtain the numerical solution of inverse nodal problem. Following that, a number of numerical examples have been given. The numerical calculations in the present paper have been conducted via pc applying some programs encoded in Matlab software.