Markov chains are an application of stochastic models in operation research, helping the analysis and optimization of processes with random events and transitions. The method that will be deployed to obtain the transient solution to a Markov chain problem is an important part of this process. The present paper introduces a novel Ordinary Differential Equation (ODE) approach to solve the Markov chain problem. The probability distribution of a continuous-time Markov chain with an infinitesimal generator at a given time is considered, which is a resulting solution of the Chapman-Kolmogorov differential equation. This study presents a one-step second-derivative method with better accuracy in solving the first-order Initial Value Problem

In this paper, a least squares group finite element method for solving coupled Burgers' problem in   2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved.  The theoretical results  show that the error estimate of this method is . The numerical results are compared with the exact solution and other available literature when the convection-dominated case to illustrate the effic

Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

Friction stir spot welding (FSSW) is a relatively new welding process that may have significant advantages compared to the fusion processes as follows joining of conventionally non-fusion weldable alloys, reduced distortion and improved mechanical properties of weldable alloys joints due to the pure solidstate joining of metals. In this paper, a three-dimensional model based on finite element analysis is used to study the thermal history in the spot-welding of aluminum alloy 2024. The model take place the thermomechanical property on the process of the welded metals. The thermal history and the evolution results with numerical model at the measured point in the friction stirred spot weld have a good matching, then the prediction of the t

Introduction: In recent decades, the endovascular treatment of cerebral arteriovenous malformations (AVMs) has advanced. However, it still carries risks of unanticipated complications. Coil migration is a reported complication of aneurysmal coiling procedures. Herein, we report a case of early intraprocedural coil migration during pressure cooker technique embolization of right thalamic AVM, discussing the management and potential explanations. The literature showed no report of coil migration after the pressure cooker technique in the form of coil-augmented Onyx injection technique (CAIT). Case description: An otherwise healthy 26-year-old female suddenly developed a severe headache with no loss of consciousness. Computed tomograp

Given the importance of increasing economic openness transport companies’ face various issues arising at present time, this required importing different types of goods with different means of transport. Therefore, these companies pay great attention to reducing total costs of transporting commodities by using numbers means of transport methods from their sources to the destinations. The majority of private companies do not acquire the knowledge of using operations research methods, especially transport models, through which the total costs can be reduced, resulting in the importance and need to solve such a problem. This research presents a proposed method for the sum of Total Costs (Tc) of rows and columns, in order to arrive at the init

Energy savings are very common in IoT sensor networks because IoT sensor nodes operate with their own limited battery. The data transmission in the IoT sensor nodes is very costly and consume much of the energy while the energy usage for data processing is considerably lower. There are several energy-saving strategies and principles, mainly dedicated to reducing the transmission of data. Therefore, with minimizing data transfers in IoT sensor networks, can conserve a considerable amount of energy. In this research, a Compression-Based Data Reduction (CBDR) technique was suggested which works in the level of IoT sensor nodes. The CBDR includes two stages of compression, a lossy SAX Quantization stage which reduces the dynamic range of the

This study aims to develop a recommendation engine methodology to enhance the model’s effectiveness and efficiency. The proposed model is commonly used to assign or propose a limited number of developers with the required skills and expertise to address and resolve a bug report. Managing collections within bug repositories is the responsibility of software engineers in addressing specific defects. Identifying the optimal allocation of personnel to activities is challenging when dealing with software defects, which necessitates a substantial workforce of developers. Analyzing new scientific methodologies to enhance comprehension of the results is the purpose of this analysis. Additionally, developer priorities were discussed, especially th