مجله بین المللی محاسبات و مدل سازی ریاضی
سال نهم شماره 4 (Autumn 2019)

The current research develops derivative-free family with memory methods with 100% improvement in the order of convergence. They have three parameters. The parameters are approximated and increase the convergence order from 4 to 6, 7, 7.5 and 8, respectively. Additionally, the new self-accelerating parameters are constructed by a new way. They have the properties of simple structures and they are calculated easily. The parameters do not increase the computational cost of the iterative methods. Numerical examples of the new schemes are given to support the theoretical results.

In this paper, we establish integral inequalities of Hermite-Hadamard type for multiplicativelys-preinvex functions. We also obtain some new inequalities involving multiplicative integralsby using some properties of multiplicatively s-preinvex and preinvex functions.

In this paper, the mathematical model of HIV infection for CD8+ T-cells is illustrated. The homotopy analysis method and the Laplace transformations are combined for solving this model. Also, the convergence theorem is proved to demonstrate the abilities of presented method for solving non-linear mathematical models. The numerical results for $N=5, 10$ are presented. Several $hbar$-curves are plotted to show the convergence regions of solutions. The plots of residual error functions indicate the precision of presented method.

The present work approaches the problem of achieving the approximate solution of the second order initial value problems (IVPs) via its conversion into a Volterra integral equation of the second kind (VIE2). Therefore, we initially solve the IVPs using Runge–Kutta of the forth–order method (RK), and then convert it into VIE2, and apply the εmodified block–pulse functions (εMBPFs) and their operational matrix for solving VIE2, which can be transformed to a lower triangular system of algebric equations. Numerical examples show that the proposed scheme has a suitable degree of accuracy.

In this manuscript, a new class of extended (m1,m2)-convex and concave functions is introduced. After some properties of (m1,m2)-convex functions have been given, the inequalities obtained with Hölder and Hölder-İşcan and power-mean and improwed power-mean integral inequalities have been compared and it has been shown that the inequality with Hölder-İşcan inequality gives a better approach than with Hölder integral inequality and improwed power-mean inequality gives a better approach than with power-mean inequality.

Dynamic network data envelopment analysis (DNDEA) has attracted a lot of attention in recent years. On one hand the available models in DNDEA evaluating the performance of a DMU with interrelated processes during specified multiple periods but on the other hand they can only measure the efficiency of dynamic network structure when a supply chain structure present. For example, in the banking industry, profit is generated by using loan as a source of investment funds, and the generate profit can also be regarded as an added source. Existing models are not able to use output from different section in different period as inputs, for the next section. So we propose a dynamic network DEA model involve two-stage structure in each period. Hence, this article is composite of two-stage and dynamic DEA that is called dynamic two-stage DEA (DTDEA) model. IT has the advantages of both dynamic DEA and two-stage models. This model can be utilized to highlight those bank branch managers can be further analyzed for best practice benchmarking. A set of bank branches is used to illustrate how the new model can be utilized to characterize the direct impact of profit on branches performance. The real data is extracted from monthly released financial data of the 94 Saderat Bank branches through 1395.