International Journal of Industrial Mathematics
Volume:15 Issue: 1, Winter 2023

The convergence of thisiterative sequence is then controlled by an embedded parameter. The fastest convergence occurs for an optimal embedded parameter which maximizes a special function. This optimization problem brings a sequence with high rate of the convergence to theunique solution in the finite region where $\frac{\partial f}{\partial y}$ has to be positive.Some illustrative examples are given to confirm the validity and reliability of this constructive theory.

Gasoline causes engine knock in higher compression ratios due to having lower spontaneous ignition temperature. Natural Gas (NG) has a higher octane number and is a proper fuel in terms of anti-knock properties; however, using it as the engine fuel results in a decline in the power of the engine and increases the emission of some exhaust gases due to lower burning velocity and gaseous nature.

Integro-differential equations arise in various physical and biological problems. In this paper, a new iterative technique for solving linear Volterra-Fredholm integro-differential equation (VFIDE) has been introduced. The method is discussed in details and it is illustrated by solving some numerical examples. The approximate solution is most easily produced iteratively via the recurrence relation. Results are compared with the exact solutions, which reveal that new iteration method is very effective and convenient.

In Software Defined Network (SDN), the controller layer that is separated from the data layer is responsible for all system functionalities. However, centralized solutions suffer from single-point-of-failure and bottleneck problems. Several controllers are used to increase availability and performance in large networks to solve the aforementioned problems. One of the main concerns is finding the optimal number of controllers and their locations, which is known as an NP-hard problem. To do this, in this paper, in addition to presenting an efficient algorithm based on Garter snake algorithm (GSO), a new statistical analysis for determining the number of controllers is figured out.

‎In this paper‎, ‎we present a computational method for solving systems of Volterra and Fredholm integral equations which is a hybrid approach‎, ‎based on the third-order Chebyshev polynomials and block-pulse functions which we will refer to as (HBV)‎, ‎for short‎. ‎The existence and uniqueness of the solutions are addressed‎. ‎Some examples are provided to clarify the efficiency and accuracy of the method‎.

In this paper, we focus on obtaining an approximate solution for multi-dimensional Fredholm integral equations of second kind. An expansion method is used for treatment multi-dimensional Fredholm integral equation of second kind. This method reduces multi-dimensional integral equation to a partial differential equation. After constructing boundary conditions, this partial differential equation reduces to algebraic equation that can be solved easily with any of the usual methods. Furthermore some theorems are proved for convergence analysis. Finally, for showing the efficiency of the method we use some numerical examples

‎In this paper‎, ‎we will use the mathematical modeling of one-dimensional observers to present the notion of the \emph{relative entropy functional} for relative dynamical systems‎. ‎Also‎, ‎the invariance of the entropy of a system under topological conjugacy is generalized to the relative entropy functional‎. ‎Moreover‎, ‎from observer viewpoint‎, ‎a new version of the Jacobs Theorem is obtained‎. ‎It has been proved that relative entropy functional is equivalent to the Kolmogorov entropy for dynamical systems‎, ‎from the viewpoint of observer $ \chi_X $‎, ‎where $ \chi_X $ is the characteristic function on compact metric space $X$‎.

In This paper we discuss about the redundancy allocation problem when uncertainty exists in the problem. The innovation of this paper is the use of fuzzy universal generating function for calculating the availability of system. The system consists of component in series and for each component, elements are used in parallel. The system has the range of levels for performance from complete perfect to complete failure. Identical redundant elements are included in order to achieve a desirable reliability. The elements of each component are characterized by their cost, weight and availability. These elements are chosen from a list that available in market. To find optimum combination of elements for each component we calculate the system availability and then use proposed NSGA-III. The proposed NSGA-III heuristic determines the maximal availability system configuration base on weight constrain.