Abstract: Publication year: 2022Source: American Journal of Computational and Applied Mathematics , Volume 12, Number 1Herawati N., Saidi S., Setiawan E., Nisa K., RopiudinThe rapid development of time series data forecasting methods has resulted in many choices of methods that can be used to forecast according to the type of data. However, what needs to be considered in the selection of forecasting methods is whether the method used provides precise forecasting results or not. The high-order Chen fuzzy time series is a development of the fuzzy time series method with the determination of Fuzzy Logic Relations (FLR) which involves two or more historical data. The back propagation algorithm is one of the algorithms found in the artificial neural network method where this algorithm has a tendency to store experiential knowledge and make it ready for use. This study aims to compare the method of high-order Chen fuzzy time series and feedforward backpropagation neural network in forecasting the composite stock price index based on MSE and MAPE values. The results showed that feedforward backpropagation neural network predicts the composite stock price index better than high-order Chen fuzzy time series method with lower MSE and MAPE values.

Abstract: Publication year: 2021Source: American Journal of Computational and Applied Mathematics , Volume 11, Number 4Ahmed Salam Najat, Douglas Kwasi BoahA travelling salesperson problem is where a salesperson starts from one place, visits all other required places once and returns to the initial point such that the overall covered distance is minimized. In this thesis, the concept of Travelling Salesperson Problem has been successfully used to analyze the operating characteristics of fruits’ seller in Bolgatanga in the Upper East Region of Ghana. The fruits’ seller was interviewed to find out the usual routes traversed by her to serve her scattered customers. Based on her responses, her daily routes and the various distances between each pair of customer locations were obtained from the Lands Commission in Bolgatanga in the Upper East Region of Ghana. A matrix of the shortest distances between pairs of customer locations in meters was then constructed and solved using Version 3 of TSP Solver and Generator which is based on the Branch and Bound Algorithm. The study has determined an optimal operating path for the fruits’ seller. It has also determined an optimal daily distance for the fruits’ seller. It is recommended that the fruits’ seller should always use the determined optimal operating path so as to minimize the total distance covered daily. Also, other hawkers should make conscious efforts to find out their optimal operating paths so as to minimize the total distances covered daily.

Abstract: Publication year: 2021Source: American Journal of Computational and Applied Mathematics , Volume 11, Number 3Jay P. NarainThe neural network solution method is applied to solve coupled non-linear differential equations for a free convection problem on a stationary wall. The results show good comparison with results from other published methods. Next a finite difference equation solver is extended to three and four dimensions. The code is tested for zero Dirichlet boundary condition and mixed non-zero Dirichlet and Neumann boundary conditions cases. The results are compared with neural network solutions with satisfactory outcome. The finite difference equation has also been extended to polar coordinates to solve potential flow problem over a two-dimensional infinite cylinder. The results are excellent.

Abstract: Publication year: 2021Source: American Journal of Computational and Applied Mathematics , Volume 11, Number 3R. ThukralIn this paper we propose two four-point secant-type methods for finding simple root of nonlinear equations. The new iterative methods do not require any derivatives and has a convergence order of 1.92. Also, we have proved the convergence order of the new methods which require only one function evaluations per full iteration. In addition, numerical examples demonstrate exceptional convergence speed of the proposed methods. It is observed that the new four-point secant-type iterative methods are very effective and robust.

Abstract: Publication year: 2021Source: American Journal of Computational and Applied Mathematics , Volume 11, Number 2Samira Zouhri, Mohcine El Baroudi, Smahane SaadiCancer is a major health issue, it presents a serious threat to human life. A deep understanding of tumor cell development, genetic mutations in cancerous cell and its biological behaviour remains a persistent need. Many scientific researches suggest that the changes in genes and their proteins expression inside a tumor cell play a crucial role in stimulating the cell division (metastasis) or in restraining its division and reducing its aggressiveness. Agent-based models are computer models that aim to capture the behaviour of individuals inside an environment, they provide a practical setting for studying complex systems. We develop an agent- based model to describe the interaction between 6 agents that represent 6 types of proteins inside a tumor cell and the effect of their exchange on tumor cell motility and metastasis. The simulation results shed light on the circumstance in which the cancerous cell has a great chance to divide and multiply.

Abstract: Publication year: 2021Source: American Journal of Computational and Applied Mathematics , Volume 11, Number 3Jay P. NarainThe use of artificial neural network to solve ordinary and elliptic partial differential equations has been of considerable interest lately [1,2,3,4,5]. The error loss optimization techniques [6,7] usually reach an undesirable minimum at some point. Further convergence is usually sought with other minimization [8]. schemes. The use of BFGS scheme has been presently investigated. The simple artificial neural network [4,5] has been applied to solve problems in higher 3 to 4 dimensions with relative ease. The results show a promising trend. The potential flow over an infinite 2D cylinder in polar coordinates has also been investigated. One would expect exact comparison with analytical solution for such a simple problem. However, due to poor convergence, the use of cartesian based neural network for polar coordinate correlation becomes an issue.

Abstract: Publication year: 2021Source: American Journal of Computational and Applied Mathematics , Volume 11, Number 2Mečislovas MariūnasThis paper presents a method for determining vibration damping in a nonlinear dynamic system of one degree of freedom. It has been found that in the case of resonance, the vibrations of the dynamic system are damped not only by the force generated by the external excitation vibration velocity, but also by the forces generated by the displacements, velocities and accelerations of vibrations at other frequencies. It was found that the magnitude of the amplitude varies in the interval of one excitation cycle and the magnitude and regularity of its change depend on the ratio of resonant, parametric vibrations and external excitation force frequencies. It has been determined that the forces generated by a nonlinear dynamic system can be vibration-exciting forces at one time and vibration-damping forces at another. Studies have found that even in the case of resonances in a nonlinear dynamic system, the vibrations are damped severel hundred time more than in a linear dynamic system. Analytical methods have been developed to allow quadratic and cubic dynamic systems of nonlinearity to choose parameter values during design that would increase the damping of the system and reduce the vibration level of the developed system and ensure its safe operation. The certainty of the analytical methods presented in the article was verified by numerical calculations.

Abstract: Publication year: 2021Source: American Journal of Computational and Applied Mathematics , Volume 11, Number 2A. P. Panta, R. P. Ghimire, Dinesh Panthi, Shankar Raj PantThis paper deals with the extensive survey of the queueing system from its birth in1909 to till date. As the time passes on old-provisions cannot tackle new-problem so newconcepts have to be developed. Some of the policies that have been developed from time to time have reported. Some of the prominent techniques of solution of queueing system have also been cited. As an illustration various queueing routing formulas are given in tabular form.

Abstract: Publication year: 2021Source: American Journal of Computational and Applied Mathematics , Volume 11, Number 1D. BitsadzeThe article deals with construction of one specific scheme for approximate calculation of singular integrals and its use for numerical solutions of integral equations of some class in the sense of Cauchy principal value. Composed quadrature formulas makes it possible equal assessment for quite a wide variety of smooth closed contours.

Abstract: Publication year: 2021Source: American Journal of Computational and Applied Mathematics , Volume 11, Number 1Shiva Prakash Gupta, Urmila Pyakurel, Tanka Nath DhamalaIn a transportation network such as an evacuation planning, if we transmit the people or goods from the dangerous zones to the safety places, there are chances of loss due to death, leakage or damage. To address this issue, the generalized network flow model incorporates a gain factor on each arc, which makes it different from the classical network flow problems. The lane reversal strategy improves both flow value and also minimize the time with minimum loss. In general, the generalized dynamic contraflow problem is NP-hard, whereas, in a lossy network with symmetric transit time on anti-parallel arcs, it is solved in pseudo-polynomial time. Due to an uneven road network structure, transit time on arcs may be asymmetrical. We extend the analytical solution of generalized dynamic contraflow problem to the case of asymmetric transit time on arcs, both in discrete and continuous-time settings, and present efficient algorithms to solve it within the same complexity.