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Stability analysis and convergence rate of a two-step predictor-corrector approach for shallow water equations with source terms 带源项的浅水方程两步预测校正方法的稳定性分析和收敛速度
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023465
R. T. Alqahtani, J. Ntonga, E. Ngondiep
{"title":"Stability analysis and convergence rate of a two-step predictor-corrector approach for shallow water equations with source terms","authors":"R. T. Alqahtani, J. Ntonga, E. Ngondiep","doi":"10.3934/math.2023465","DOIUrl":"https://doi.org/10.3934/math.2023465","url":null,"abstract":"This paper deals with a two-step explicit predictor-corrector approach so-called the two-step MacCormack formulation, for solving the one-dimensional nonlinear shallow water equations with source terms. The proposed two-step numerical scheme uses the fractional steps procedure to treat the friction slope and to upwind the convection term in order to control the numerical oscillations and stability. The developed scheme uses both forward and backward difference formulations in the predictor and corrector steps, respectively. The linear stability of the constructed technique is deeply analyzed using the Von Neumann stability approach whereas the convergence rate of the proposed method is numerically obtained in the $ L^{2} $-norm. A wide set of numerical examples confirm the theoretical results.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Double total domination number of Cartesian product of paths 路径笛卡尔积的双总支配数
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023479
Linyu Li, Jun Yue, Xia Zhang
{"title":"Double total domination number of Cartesian product of paths","authors":"Linyu Li, Jun Yue, Xia Zhang","doi":"10.3934/math.2023479","DOIUrl":"https://doi.org/10.3934/math.2023479","url":null,"abstract":"A vertex set $ S $ of a graph $ G $ is called a double total dominating set if every vertex in $ G $ has at least two adjacent vertices in $ S $. The double total domination number $ gamma_{times 2, t}(G) $ of $ G $ is the minimum cardinality over all the double total dominating sets in $ G $. Let $ G square H $ denote the Cartesian product of graphs $ G $ and $ H $. In this paper, the double total domination number of Cartesian product of paths is discussed. We determine the values of $ gamma_{times 2, t}(P_isquare P_n) $ for $ i = 2, 3 $, and give lower and upper bounds of $ gamma_{times 2, t}(P_isquare P_n) $ for $ i geq 4 $.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cubic B-Spline method for the solution of the quadratic Riccati differential equation 三次b样条法求解二次Riccati微分方程
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023483
O. Ala'yed, B. Batiha, Diala Alghazo, F. Ghanim
{"title":"Cubic B-Spline method for the solution of the quadratic Riccati differential equation","authors":"O. Ala'yed, B. Batiha, Diala Alghazo, F. Ghanim","doi":"10.3934/math.2023483","DOIUrl":"https://doi.org/10.3934/math.2023483","url":null,"abstract":"The quadratic Riccati equations are first-order nonlinear differential equations with numerous applications in various applied science and engineering areas. Therefore, several numerical approaches have been derived to find their numerical solutions. This paper provided the approximate solution of the quadratic Riccati equation via the cubic b-spline method. The convergence analysis of the method is discussed. The efficiency and applicability of the proposed approach are verified through three numerical test problems. The obtained results are in good settlement with the exact solutions. Moreover, the numerical results indicate that the proposed cubic b-spline method attains a superior performance compared with some existing methods.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70187140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A space-time model for analyzing contagious people based on geolocation data using inverse graphs 一种基于地理位置数据的时空模型，利用逆图分析传染性人群
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023516
S. Merino, Juergen Doellner, Javier Martínez, F. Guzmán, R. Guzmán, Juan De Dios Lara
{"title":"A space-time model for analyzing contagious people based on geolocation data using inverse graphs","authors":"S. Merino, Juergen Doellner, Javier Martínez, F. Guzmán, R. Guzmán, Juan De Dios Lara","doi":"10.3934/math.2023516","DOIUrl":"https://doi.org/10.3934/math.2023516","url":null,"abstract":"Mobile devices provide us with an important source of data that capture spatial movements of individuals and allow us to derive general mobility patterns for a population over time. In this article, we present a mathematical foundation that allows us to harmonize mobile geolocation data using differential geometry and graph theory to identify spatial behavior patterns. In particular, we focus on models programmed using Computer Algebra Systems and based on a space-time model that allows for describing the patterns of contagion through spatial movement patterns. In addition, we show how the approach can be used to develop algorithms for finding \"patient zero\" or, respectively, for identifying the selection of candidates that are most likely to be contagious. The approach can be applied by information systems to evaluate data on complex population movements, such as those captured by mobile geolocation data, in a way that analytically identifies, e.g., critical spatial areas, critical temporal segments, and potentially vulnerable individuals with respect to contact events.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70188826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Discrete Erlang-2 distribution and its application to leukemia and COVID-19 离散Erlang-2分布及其在白血病和COVID-19中的应用
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023520
Mohamed Ahmed Mosilhy
{"title":"Discrete Erlang-2 distribution and its application to leukemia and COVID-19","authors":"Mohamed Ahmed Mosilhy","doi":"10.3934/math.2023520","DOIUrl":"https://doi.org/10.3934/math.2023520","url":null,"abstract":"Via the survival discretization method, this research revealed a novel discrete one-parameter distribution known as the discrete Erlang-2 distribution (DE2). The new distribution has numerous surprising improvements over many conventional discrete distributions, particularly when analyzing excessively dispersed count data. Moments and moments-generating functions, a few descriptive measures (central tendency and dispersion), monotonicity of the probability mass function, and the hazard rate function are just a few of the statistical aspects of the postulated distribution that have been developed. The single parameter of the DE2 distribution was estimated via the maximum likelihood technique. Real-world datasets, leukemia and COVID-19, were applied to analyze the effectiveness of the recommended distribution.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70188894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A review on portfolio optimization models for Islamic finance 伊斯兰金融投资组合优化模型综述
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023523
Doong Toong Lim, K. Goh, Y. Sim
{"title":"A review on portfolio optimization models for Islamic finance","authors":"Doong Toong Lim, K. Goh, Y. Sim","doi":"10.3934/math.2023523","DOIUrl":"https://doi.org/10.3934/math.2023523","url":null,"abstract":"The era of modern portfolio theory began with the revolutionary approach by Harry Markowitz in 1952. However, several drawbacks of the model have rendered it impractical to be used in reality. Thus, various modifications have been done to refine the classical model, including concerns about risk measures, trading practices and computational efficiency. On the other hand, Islamic finance is proven to be a viable alternative to the conventional system following its outstanding performance during the financial crisis in 2008. This emerging sector has gained a lot of attention from investors and economists due to its significantly increasing impact on today's economy, corresponding to globalization and a demand for a sustainable investment strategy. A comprehensive literature review of the notable conventional and Islamic models is done to aid future research and development of portfolio optimization, particularly for Islamic investment. Additionally, the study provides a concisely detailed overview of the principles of Islamic finance to prepare for the future development of an Islamic finance model. Generally, this study outlines the comprehensive features of portfolio optimization models over the decades, with an attempt to classify and categorize the advantages and drawbacks of the existing models. The trend of portfolio optimization modelling can be captured by gathering and recording the problems and solutions of the reviewed models.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70189076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Iterative schemes for numerical reckoning of fixed points of new nonexpansive mappings with an application 新非扩张映射不动点数值推算的迭代格式及其应用
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023543
K. Ullah, Junaid Ahmad, H. Hammad, R. George
{"title":"Iterative schemes for numerical reckoning of fixed points of new nonexpansive mappings with an application","authors":"K. Ullah, Junaid Ahmad, H. Hammad, R. George","doi":"10.3934/math.2023543","DOIUrl":"https://doi.org/10.3934/math.2023543","url":null,"abstract":"The goal of this manuscript is to introduce a new class of generalized nonexpansive operators, called $ (alpha, beta, gamma) $-nonexpansive mappings. Furthermore, some related properties of these mappings are investigated in a general Banach space. Moreover, the proposed operators utilized in the $ K $-iterative technique estimate the fixed point and examine its behavior. Also, two examples are provided to support our main results. The numerical results clearly show that the $ K $-iterative approach converges more quickly when used with this new class of operators. Ultimately, we used the $ K $-type iterative method to solve a variational inequality problem on a Hilbert space.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70189874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Pricing of vulnerable options based on an uncertain CIR interest rate model 基于不确定CIR利率模型的脆弱期权定价
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023563
Guiwen Lv, Ping Xu, Yanxue Zhang
{"title":"Pricing of vulnerable options based on an uncertain CIR interest rate model","authors":"Guiwen Lv, Ping Xu, Yanxue Zhang","doi":"10.3934/math.2023563","DOIUrl":"https://doi.org/10.3934/math.2023563","url":null,"abstract":"The traditional Cox-Ingersoll-Ross (CIR) interest rate model follows a stochastic differential equation that cannot obtain the closed solution while the uncertain CIR interest rate model is an uncertain differential equation. First, this paper gives the solution in terms of the distribution of the uncertain CIR interest rate model based on uncertainty theory. Second, the pricing formulas of vulnerable European call option and vulnerable European put option are obtained by using the uncertain CIR interest rate model. Finally, according to the proposed pricing formula, the corresponding numerical algorithms are designed and several numerical examples are given to verify the effectiveness of the algorithm. Our results not only enrich the option pricing theory, but they also have a certain guiding significance for the derivatives market.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70190904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Exponential sums involving the divisor function over arithmetic progressions 包含除数函数的等差数列的指数和
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023561
Rui Zhang, Y. Li, Xiao-Hui Yan
{"title":"Exponential sums involving the divisor function over arithmetic progressions","authors":"Rui Zhang, Y. Li, Xiao-Hui Yan","doi":"10.3934/math.2023561","DOIUrl":"https://doi.org/10.3934/math.2023561","url":null,"abstract":"Let $ phi(x) $ be a smooth function supported on $ [1, 2] $ with derivatives bounded by $ phi^{(j)}(x)ll 1 $ and $ d_3(n) $ be the number of ways to write $ n $ as a product of three factors. We get the asymptotic formula for the nonlinear exponential sum $ sumlimits_{n equiv l mod q}d_3(n)phileft(frac{n}{X}right)eleft(frac{3sqrt[3]{kn}}{q}right) $.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70191125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonlinear robust control of trajectory-following for autonomous ground electric vehicles with active front steering system 具有主动前转向系统的自主地面电动汽车轨迹跟踪的非线性鲁棒控制
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023565
Xianjian Jin, Qikang Wang, Zeyuan Yan, Hang Yang
{"title":"Nonlinear robust control of trajectory-following for autonomous ground electric vehicles with active front steering system","authors":"Xianjian Jin, Qikang Wang, Zeyuan Yan, Hang Yang","doi":"10.3934/math.2023565","DOIUrl":"https://doi.org/10.3934/math.2023565","url":null,"abstract":"This paper presents a nonlinear robust H-infinity control strategy for improving trajectory following performance of autonomous ground electric vehicles (AGEV) with active front steering system. Since vehicle trajectory dynamics inherently influenced by various driving maneuvers and road conditions, the main objective is to deal with the trajectory following control challenges of parametric uncertainties, system nonlinearities, and external disturbance. The AGEV system dynamics and its uncertain vehicle trajectory following system are first modeled and constructed, in which parameter uncertainties related to the physical limits of tire are considered and handled, then the control-oriented vehicle trajectory following augmented system with dynamic error is developed. The resulting nonlinear robust H-infinity state-feedback controller (NHC) of vehicle trajectory-following system is finally designed by H-infinity performance index and nonlinear compensation under AGEV system requirements, and solved utilizing a set of linear matrix inequalities derived from quadratic H-infinity performance and Lyapunov stability. Simulations for double lane change and serpentine scenes are carried out to verify the effectiveness of the proposed controller with a high-fidelity, CarSim®, full-vehicle model. It is found from the results that the proposed NHC provides improved vehicle trajectory following performance compared with the linear quadratic regulator (LQR) controller and robust H-infinity state-feedback controller (RHC).","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70191207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
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