Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697714Issue 220240601Quantum solutions of a nonlinear Schrödinger equation3303464471210.22067/ijnao.2023.84855.1324ENS. ArfaouiLaboratory of Algebra, Number Theory and Nonlinear Analysis, Department of Math-ematics, Faculty of Sciences, University of Monastir, Avenue of the Environment, 5019 Monastir, Tunisia.nstitut Supérieur d’Informatique du Kef, Université de Jendouba, 5 Rue Saleh Ayech - 7100 Kef, TunisiaBen MabroukLaboratory of Algebra, Number Theory and Nonlinear Analysis, Department of Math- ematics, Faculty of Sciences, University of Monastir, Avenue of the Environment, 5019 Monastir, Tunisia.Department of Mathematics, Higher Institute of Applied Mathematics and Computer
Science, University of Kairouan, Street Assad Ibn Alfourat, Kairouan 3100, Tunisia.Department of Mathematics, Faculty of Sciences, University of Tabuk, King Faisal Road, Tabuk 47512, Saudi Arabia.0000-0002-2571-1066Journal Article20231013In the present paper, we precisely conduct a quantum calculus method for the numerical solutions of PDEs. A nonlinear Schrödinger equation is considered. Instead of the known classical discretization methods based on the finite difference scheme, Adomian method, and third modified ver-sions, we consider a discretization scheme leading to subdomains according to q-calculus and provide an approximate solution due to a specific value of the parameter q. Error estimates show that q-calculus may produce effi-cient numerical solutions for PDEs. The q-discretization leads effectively to higher orders of convergence provided with faster algorithms. The numer-ical tests are applied to both propagation and interaction of soliton-type solutions.https://ijnao.um.ac.ir/article_44712_8453d26e016c1a55f916f63d8f3a50bc.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697714Issue 220240601Discontinuous Galerkin approach for two-parametric convection-diffusion equation with discontinuous source term3473664473310.22067/ijnao.2024.84456.1316ENK. R. RanjanDepartment of Mathematics, National Institute of Technology Patna, Patna, India.0000-0001-9320-4018S. GowrisankarDepartment of Mathematics, National Institute of Technology Patna, Patna, India.0000-0002-0007-0477Journal Article20230915In this article, we explore the discontinuous Galerkin finite element method for two-parametric singularly perturbed convection-diffusion problems with a discontinuous source term. Due to the discontinuity in the source term, the problem typically shows a weak interior layer. Also, the presence of multiple perturbation parameters in the problem causes boundary layers on both sides of the boundary. In this work, we develop the nonsymmetric discontinuous Galerkin finite element method with interior penalties to handle the layer phenomenon. With the use of a typical Shishkin mesh, the domain is discretized, and a uniform error estimate is obtained. Numerical experiments are conducted to validate the theoretical conclusions.https://ijnao.um.ac.ir/article_44733_44ab553ad927bda0eb1430bde393e776.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697714Issue 220240601High order second derivative multistep collocation methods for ordinary differential equations3673904480710.22067/ijnao.2024.85789.1358ENS. FazeliMarand Technical Faculty, University of Tabriz, Tabriz, Iran.0000-0001-9772-7051Journal Article20231215In this paper, we introduce second derivative multistep collocation meth-ods for the numerical integration of ordinary differential equations (ODEs). These methods combine the concepts of both multistep methods and col-location methods, using second derivative of the solution in the collocation points, to achieve an accurate and efficient solution with strong stability properties, that is, A-stability for ODEs. Using the second-order deriva-tives leads to high order of convergency in the proposed methods. These methods approximate the ODE solution by using the numerical solution in some points in the r previous steps and by matching the function values and its derivatives at a set of collocation methods. Also, these methods utilize information from the second derivative of the solution in the colloca-tion methods. We present the construction of the technique and discuss the analysis of the order of accuracy and linear stability properties. Finally, some numerical results are provided to confirm the theoretical expecta-tions. A stiff system of ODEs, the Robertson chemical kinetics problem, and the two-body Pleiades problem are the case studies for comparing the efficiency of the proposed methods with existing methods.https://ijnao.um.ac.ir/article_44807_9ee8d35bbc6bd904ffe2016f2685f4ef.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697714Issue 220240601Jarratt and Jarratt-variant families of iterative schemes for scalar and system of nonlinear equations3914164493110.22067/ijnao.2024.84415.1314ENO. OgbereyivweDepartment of Mathematics and Statistics, Delta State University of Science and Technology, Delta State, Nigeria.0000-0001-9810-2299E. J. AtajeromavwoDepartment of Software Engineering, Delta State University of Science and Technology, Delta State, Nigeria.S. S. UmarDepartment of Statistics, Federal Polytechnic, Auchi, Nigeria.Journal Article20230912This manuscript puts forward two new generalized families of Jarratt’s iterative schemes for deciding the solution of scalar and systems of non-linear equations. The schemes involve weight functions that are based on bi-variate rational approximation polynomial of degree two in both its numerator and denominator. The convergence study conducted on the schemes, indicated that they have convergence order (CO) four in scalar space and retain the same number of CO in vector space. The numerical experiments conducted on the schemes when used to decide the solutions of some real-life nonlinear models show that they are good challengers of some well-known and robust existing iterative schemes.https://ijnao.um.ac.ir/article_44931_f01a5d6b397a4508dd6c689a160f9e6a.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697714Issue 220240601An innovative particle physics optimization algorithm for efficient test case minimization in software testing4174484476710.22067/ijnao.2024.85066.1333ENU. JaiswalDepartment of Computer Science Engineering and Information Technology, Jaypee In-stitute of Information Technology Noida, India.0009-0002-1572-8275A. PrajapatiDepartment of Computer Science Engineering and Information Technology, Jaypee In-stitute of Information Technology Noida, India.Journal Article20231101Software testing is a crucial step in the development of software that guar-antees the dependability and quality of software products. A crucial step in software testing is test case minimization, which seeks to minimize the number of test cases while ensuring maximum coverage of the system being tested. It is observed that the existing algorithms for test case minimization still suffer in efficiency and precision. This paper proposes a new optimiza-tion algorithm for efficient test case minimization in software testing. The proposed algorithm is designed on the base parameters of the metaheuristic algorithms, inspired by scientific principles. We evaluate the performance of the proposed algorithm on a benchmark suite of test cases from the literature. Our experimental results show that the proposed algorithm is highly effective in reducing the number of test cases while maintaining high coverage of the system under test. The algorithm outperforms the existing optimization algorithms in terms of efficiency and accuracy. We also con-duct a sensitivity analysis to investigate the effect of different parameters on the performance of the proposed algorithm. The sensitivity analysis results show that the performance of the algorithm is robust to changes in the parameter values. The proposed algorithm can help software testers reduce the time and effort required for testing while ensuring maximum coverage of the system under test.https://ijnao.um.ac.ir/article_44767_19f7086f1884f4f446f416be8270a6f3.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697714Issue 220240601Dynamics of Cholera Pathogen Carriers and Effect of Hygiene Consciousness in Cholera Outbreaks4494744492310.22067/ijnao.2024.82434.1269ENS.F. AbubakarDepartment of Mathematics, Faculty of Physical Sciences, Kebbi State University of Science and Technology, Aliero, Nigeria.0000-0002-8238-8197M.O. IbrahimDepartment of Mathematics, Faculty of Physical Sciences, University of Ilorin, Ilorin, Nigeria,0000-0002-0498-6060Journal Article20230524We derive a deterministic mathematical model that scrutinizes the dy-namics of cholera pathogen carriers and the hygiene consciousness of in-dividuals, before the illness, during its prevalence, and after the disease’s outbreaks. The dynamics can effectively help in curtailing the disease, but its effects had less coverage in the literature. Boundedness of the solu-tion of the model, its existence, and uniqueness are ascertained. Effects of cholera pathogen carriers and hygiene consciousness of individuals in controlling the disease or allowing its further spread are analyzed. The differential transformation method is used to obtain series solutions of the differential equations that make the system of the model. Simulations of the series solutions of the model are carried out and displayed in graphs. The dynamics of the concerned state variables and parameters in the model are interpreted via the obtained graphs. It is observed that higher hygiene consciousness of individuals can drastically reduce catching cholera disease at onset and further spread of its infections in the population, this in turn, shortens the period of cholera epidemic.https://ijnao.um.ac.ir/article_44923_568dc8b913b840390619aa37c1e9d05f.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697714Issue 220240601Drug release from a two-layer stent coating considering the viscoelastic property of the arterial wall: A mathematical and numerical study4754994496310.22067/ijnao.2024.85218.1335ENE. AzhdariDepartment of Mathematics, Salman Farsi University of Kazerun, Iran.A. EmamiDepartment of Mathematics, Salman Farsi University of Kazerun, Iran.Journal Article20231106Atherosclerosis is one of the most common diseases in the world. Med-ication with metal stents plays an important role in treating this disease. There are many models for delivering drugs from stents to the arterial wall. This paper presents a model that describes drug delivery from the stent coating layers to the arterial wall tissue. This model complements the previous models by considering the mec hanical properties of the arte-rial wall tissue, which changes due to atherosclerosis and improves results for designing stents. The stability behavior of the model is analyzed, and a number of numerical results are provided with explanations. A compar-ison between numerical and experimental results, which examine a more accurate match between the in vivo and in vitro, is shown.https://ijnao.um.ac.ir/article_44963_227e70eb183601b8509cd4ac78180402.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697714Issue 220240601Mathematical analysis and forecasting of controlled Spatio-temporal dynamics of the EG.5 Virus5005214494310.22067/ijnao.2024.85581.1349ENE.M. MoumineLaboratory of Analysis, Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of science Ben M’sik, University Hassan II, Casablanca, Morocco.0000-0003-4801-4252O. BalatifLaboratory of Fundamental Mathematics and Their Applications , Department of Mathematics Faculty of Sciences El Jadida, Chouaib Doukkali University, El Jadida, Morocco.University, El Jadida, Morocco.0000-0003-1887-5350M. RachikLaboratory of Analysis, Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of science Ben M’sik, University Hassan II, Casablanca, Morocco.0000-0002-5118-2786Journal Article20231127In this article, we propose a mathematical approach that connects an innovative spatio-temporal model to the problem of the EG.5 variant of COVID-19 in a human population. We demonstrate the existence and uniqueness of the global positive solution for our suggested system. The implementation and analysis of an applicable optimal control issue are as follows. The methods of optimal control theory are applied in this work to demonstrate the existence of optimal control, and with necessary op-timality conditions, we discover the explicit expression of optimal control that minimizes the negative impacts of this infectious disease on countries. We provide numerical simulations at the conclusion to demonstrate the efficacy of our chosen strategy.https://ijnao.um.ac.ir/article_44943_e8089100d66f4ef63989021444293858.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697714Issue 220240601Optimizing natural gas liquids (NGL) production process: A multi-objective approach for energy-efficient operations using genetic algorithm and artificial neural networks5225444503010.22067/ijnao.2024.83955.1303ENN. SabeghiDepartment of Mathematics, Faculty of Basic Sciences, Velayat University, Iranshahr, Iran.B. Kiani TalaeiUniversity of Sistan and Baluchestan, Zahedan, Iran.R. GhanbariFerdowsi university of Mashhad, Mashhad, Iran.K. Ghorbani-MoghadamMosaheb Institute of Mathematics, Kharazmi University, Tehran, Iran.Journal Article20230815There are various techniques for separating natural gas liquid (NGL) from natural gas, one of which is refrigeration. In this method, the temper-ature is reduced in the dew point adjustment stage to condense the NGLs. The purpose of this paper is to introduce a methodology for optimizing the NGLs production process by determining the optimal values for specific set-points such as temperature and pressure in various vessels and equip-ment. The methodology also focuses on minimizing energy consumption during the NGL production process. To do this, this research defines a multi-objective problem and presents a hybrid algorithm, including a ge-netic algorithm (NSGA II) and artificial neural network (ANN) system. We solve the defined multi-objective problem using NSGA II. In order to de-sign a tool that is a decision-helper for selecting the appropriate set-points, the ability of the ANN algorithm along with multi-objective optimization is evaluated. We implement our proposed algorithm in an Iranian chemical factory, specifically the NGL plant, which separates NGL from natural gas, as a case study for this article. Finally, we demonstrate the effectiveness of our proposed algorithm using the nonparametric statistical Kruskal–Wallis test.https://ijnao.um.ac.ir/article_45030_e032bef5d57a0cb52cc79a8393581934.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697714Issue 220240601A new bi-level data envelopment analysis model to evaluate the Human Development Index5455794495210.22067/ijnao.2024.82197.1252ENE. HajinezhadSchool of Mathematics, Iran University of Science and Technology, Tehran, Iran.H. HajinezhadDepartment of Mathematics, Payame Noor University, Tehran, Iran.M.R. AlirezaeeSchool of Mathematics, Iran University of Science and Technology, Tehran, Iran.Journal Article20230504In the 1990s, the united nations development programme (UNDP) in-troduced the human development index (HDI) to determine the develop-ment degrees of countries. One deficiency in the HDI calculation is the use of equal weights for its sub-indicators. Many scholars have tried to solve this problem using a data envelopment analysis (DEA) method, particu-larly the one enhanced by weight restrictions. Indeed no specific methodhas been yet suggested to determine the parameters of the weight restric-tions. In this paper, we use four DEA/benefit of the doubt (BoD) models enriched by the assurance regions type I (AR-I) constraints to assess human development; we aim to objectively determine the AR-I bounds. Therefore, we consider a basis as the accepted human development values and propose a bi-level optimization problem to extract the AR-I bounds in such a way that the efficiency scores are almost the same as the basic values. On the other hand, the HDI is a globally accepted index that shows small changes year by year. So, if the UNDP decides to apply a BoD model for calculat-ing the HDI instead of the traditional method, then it is better than the scores obtained by the BoD model, showing small changes in comparison with the HDI, at least in the first few years. Therefore, the HDI values are considered as the basis. Moreover, the objectively achieved AR-I bounds provide us with an insight into the way the sub-indicators affect the de-velopment scores. The bounds can be modified by the experts opinions, in the future.https://ijnao.um.ac.ir/article_44952_2cb6755be5cc6ca9b171ae4c2cda2ea1.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697714Issue 220240601Modeling individual mobility’s impact on COVID-19 transmission: Insights from a two-patch SEIR-V approach5806124503110.22067/ijnao.2024.85987.1365ENM. BouzianeDepartment of Mathematics, Higher Normal School of Mostaganem, Mostaganem 27000, Algeria.M.A. BoubekeurDepartment of Mathematics and Computer Science, Abdelhamid Ben Badis University, Mostaganem 27000, Algeria.M.E.B. KeddarDepartment of Mathematics and Computer Science, Abdelhamid Ben Badis University, Mostaganem 27000, Algeria.O. BelhamitiDepartment of Mathematics and Computer Science, Abdelhamid Ben Badis University, Mostaganem 27000, Algeria.0000-0002-6514-2769Journal Article20231220This research explores the influence of individual mobility on COVID-19 transmission, utilizing a temporal mathematical model to clarify disease spread and vaccination dynamics across diverse regions. Employing a com-putationally efficient two-patch configuration that emphasizes regional in-teractions, our study aims to guide optimal disease control strategies. The introduced SEIR-V model with a two-patch setup estimates the vaccination reproduction number, Rv, while equilibrium points and system stability are identified. Visualizations from numerical simulations and sensitivity analyses illustrate key parameters affecting the vaccination reproduction number and COVID-19 control measures. Our findings underscore system responsiveness, emphasizing the intricate relationship between Rv , migra-tion rates, and disease prevalence.https://ijnao.um.ac.ir/article_45031_496687ea554517f1725d09b73583e525.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697714Issue 220240601Goursat problem in Hyperbolic partial differential equations with variable coefficients solved by Taylor collocation method6136374505710.22067/ijnao.2024.85895.1364ENF. BiremLaboratory of Mathematics and their interactions, University Center Abdelhafid Boussouf, Mila, Algeria.0000-0002-5362-7646A. BoulmerkaLaboratory of Mathematics and their interactions, University Center Abdelhafid Boussouf, Mila, Algeria.0000-0003-4920-1850H. LaibLaboratory of Mathematics and their interactions, University Center Abdelhafid Boussouf, Mila, Algeria.0000-0001-9935-9512C. HennousLaboratory of Mathematics and their interactions, University Center Abdelhafid Boussouf, Mila, Algeria.0009-0007-2230-0679Journal Article20231217The hyperbolic partial differential equation (PDE) has important practical uses in science and engineering. This article provides an estimate for solving the Goursat problem in hyperbolic linear PDEs with variable coefficients. The Goursat PDE is transformed into a second kind of linear Volterra in-tegral equation. A convergent algorithm that employs Taylor polynomials is created to generate a collocation solution, and the error using the maxi-mum norm is estimated. The paper includes numerical examples to prove the method’s effectiveness and precision.https://ijnao.um.ac.ir/article_45057_4a6674924a6fd1724f19657e3f4e9232.pdf