In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

Transportation and distribution are the most important elements in the work system for any company, which are of great importance in the success of the chain work. Al-Rabee factory is one of the largest ice cream factories in Iraq and it is considered one of the most productive and diversified factories with products where its products cover most areas of the capital Baghdad, however, it lacks a distribution system based on scientific and mathematical methods to work in the transportation and distribution processes, moreover, these processes need a set of important data that cannot in any way be separated from the reality of fuzziness industrial environment in Iraq, which led to use the fuzzy sets theory to reduce the levels of uncertainty.

this paper presents a novel method for solving nonlinear optimal conrol problems of regular type via its equivalent two points boundary value problems using the non-classical

This article studies the nonlocal inverse boundary value problem for a rectangular domain, a second-order, elliptic equation and a two-dimensional equation. The main objective of the article is to find the unidentified coefficient and provide a solution to the problem. The two-dimensional second-order, convection equation is solved directly using the finite difference method (FDM). However, the inverse problem was successfully solved the MATLAB subroutine lsqnonlin from the optimization toolbox after reformulating it as a nonlinear regularized least-square optimization problem with a simple bound on the unknown quantity. Considering that the problem under study is often ill-posed and that even a small error in the input data can hav

Wireless Body Area Network (WBAN) is a tool that improves real-time patient health observation in hospitals, asylums, especially at home. WBAN has grown popularity in recent years due to its critical role and vast range of medical applications. Due to the sensitive nature of the patient information being transmitted through the WBAN network, security is of paramount importance. To guarantee the safe movement of data between sensor nodes and various WBAN networks, a high level of security is required in a WBAN network. This research introduces a novel technique named Integrated Grasshopper Optimization Algorithm with Artificial Neural Network (IGO-ANN) for distinguishing between trusted nodes in WBAN networks by means of a classifica

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

In this study, the energy charging mechanism is mathematically modeled to determine the impact of design modifications on the thermofluidic behavior of a phase change material (PCM) filled in a triplex tube containment geometry. The surface area of the middle tube, where the PCM is placed, is supported by single or multi-internal frustum tubes in vertical triplex tubes to increase the performance of the heating and cooling of the system. In addition to the ordinary straight triplex tubes, three more scenarios are considered: (1) changing the middle tube to the frustum tube, (2) changing the inner tube to the frustum tube, and (3) changing both the internal and central tubes to the frustum tubes. The impact of adopting the tube desig