This paper presents a newly developed method with new algorithms to find the numerical solution of nth-order state-space equations (SSE) of linear continuous-time control system by using block method. The algorithms have been written in Matlab language. The state-space equation is the modern representation to the analysis of continuous-time system. It was treated numerically to the single-input-single-output (SISO) systems as well as multiple-input-multiple-output (MIMO) systems by using fourth-order-six-steps block method. We show that it is possible to find the output values of the state-space method using block method. Comparison between the numerical and exact results has been given for some numerical examples for solving different type

    Fuzzy numbers are used in various fields such as fuzzy process methods, decision control theory, problems involving decision making, and systematic reasoning. Fuzzy systems, including fuzzy set theory. In this paper, pentagonal fuzzy variables (PFV) are used to formulate linear programming problems (LPP). Here, we will concentrate on an approach to addressing these issues that uses the simplex technique (SM). Linear programming problems (LPP) and linear programming problems (LPP) with pentagonal fuzzy numbers (PFN) are the two basic categories into which we divide these issues. The focus of this paper is to find the optimal solution (OS) for LPP with PFN on the objective function (OF) and right-hand side. New ranking f

           In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

In this paper, the reliability and scheduling of maintenance of some medical devices were estimated by one variable, the time variable (failure times) on the assumption that the time variable for all devices has the same distribution as (Weibull distribution.

The method of estimating the distribution parameters for each device was the OLS method.

The main objective of this research is to determine the optimal time for preventive maintenance of medical devices. Two methods were adopted to estimate the optimal time of preventive maintenance. The first method depends on the maintenance schedule by relying on information on the cost of maintenance and the cost of stopping work and acc

In this paper, by using the Banach fixed point theorem, we prove the existence and uniqueness theorem of a fractional Volterra integral equation in the space of Lebesgue integrable 𝐿1(𝑅+) on unbounded interval [0,∞).

     This paper is used for solving component Volterra nonlinear systems by means of the combined Sumudu transform with Adomian decomposition process. We equate the numerical results with the exact solutions to demonstrate the high accuracy of the solution results. The results show that the approach is very straightforward and effective.

Let be a Banach space, be a nonempty closed convex subset of , and be self
nonexpansive map. The sequence generated by the iterative method
, where be a contractive mapping
and is a sequence in We generalize the mapping to non-sel -Strongly
Pseudocontractive .

The influence of an aortic aneurysm on blood flow waveforms is well established, but how to exploit this link for diagnostic purposes still remains challenging. This work uses a combination of experimental and computational modelling to study how aneurysms of various size affect the waveforms. Experimental studies are carried out on fusiform-type aneurysm models, and a comparison of results with those from a one-dimensional fluid–structure interaction model shows close agreement. Further mathematical analysis of these results allows the definition of several indicators that characterize the impact of an aneurysm on waveforms. These indicators are then further studied in a computational model of a systemic blood flow network. This demonstr

Many of the dynamic processes in different sciences are described by models of differential equations. These models explain the change in the behavior of the studied process over time by linking the behavior of the process under study with its derivatives. These models often contain constant and time-varying parameters that vary according to the nature of the process under study in this We will estimate the constant and time-varying parameters in a sequential method in several stages. In the first stage, the state variables and their derivatives are estimated in the method of penalized splines(p- splines) . In the second stage we use pseudo lest square to estimate constant parameters, For the third stage, the rem