توجه: محتویات این صفحه به صورت خودکار پردازش شده و مقاله‌های نویسندگانی با تشابه اسمی، همگی در بخش یکسان نمایش داده می‌شوند.
۱The analysis of a disease–free equilibrium of Hepatitis B model
اطلاعات انتشار: Sahand Communications in Mathematical Analysis، سوم،شماره۲، ۲۰۱۶، سال
تعداد صفحات: ۱۱
In this paper we study the dynamics of Hepatitis B virus (HBV) infection under administration of a vaccine and treatment, where the disease is transmitted directly from the parents to the offspring and also through contact with infective individuals. Stability of the disease–free steady state is investigated. The basic reproductive rate, R0, is derived. The results show that the dynamics of the model is completely determined by the basic reproductive number R0. If R01, the disease–free equilibrium is globally stable and the disease always dies out and if R0>1 , the disease–free equilibrium is unstable and the disease is uniformly persistent.

۲A two–phase variable neighborhood search for solving nonlinear optimal control problems
اطلاعات انتشار: Iranian Journal of Numerical Analysis and Optimization، پنجم،شماره۱، ۲۰۱۵، سال
تعداد صفحات: ۲۴
In this paper, a two–phase algorithm, namely IVNS, is proposed for solving nonlinear optimal control problems. In each phase of the algorithm, we use a variable neighborhood search (VNS), which performs a uniform distribution in the shaking step and the successive quadratic programming, as the local search step. In the first phase, VNS starts with a completely random initial solution of control input values. To increase the accuracy of the solution obtained from the phase 1, some new time nodes are added and the values of the new control inputs are estimated by spline interpolation. Next, in the second phase, VNS restarts by the solution constructed by the phase 1. The proposed algorithm is implemented on more than 20 well–known benchmarks and real world problems, then the results are compared with some recently proposed algorithms. The numerical results show that IVNS can find the best solution on 84% of test problems. Also, to compare the IVNS with a common VNS (when the number of time nodes is same in both phases), a computational study is done. This study shows that IVNS needs less computational time with respect to common VNS, when the quality of solutions are not different signifcantly.

۳Two numerical methods for nonlinear constrained quadratic optimal control problems using linear B–spline functions
اطلاعات انتشار: Iranian Journal of Numerical Analysis and Optimization، ششم،شماره۲، ۲۰۱۶، سال
تعداد صفحات: ۲۲
This paper presents two numerical methods for solving the nonlinear constrained optimal control problems including quadratic performance index. The methods are based upon linear B–spline functions. The properties of B–spline functions are presented. Two operational matrices of integration are introduced for related procedures. These matrices are then utilized to reduce the solution of the nonlinear constrained optimal control to a nonlinear programming one to which existing well–developed algorithms may be applied. Illustrative examples are included to demonstrate the validity and applicability of the presented techniques.
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