Computational and Mathematical Methods最新文献_第10页

On the local convergence of efficient Newton-type solvers with frozen derivatives for nonlinear equations 非线性方程具有冻结导数的有效牛顿型解的局部收敛性

Computational and Mathematical Methods Pub Date : 2021-08-02 DOI: 10.1002/cmm4.1184

Ramandeep Behl, Ioannis K. Argyros, Christopher I. Argyros

{"title":"On the local convergence of efficient Newton-type solvers with frozen derivatives for nonlinear equations","authors":"Ramandeep Behl, Ioannis K. Argyros, Christopher I. Argyros","doi":"10.1002/cmm4.1184","DOIUrl":"10.1002/cmm4.1184","url":null,"abstract":"The aim of this article is to study the local convergence of a generalized <math>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>+</mo>\u0000 <mn>2</mn>\u0000 </mrow></math>-step solver with nondecreasing order of convergence <math>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 <mi>m</mi>\u0000 <mo>+</mo>\u0000 <mn>3</mn>\u0000 </mrow></math>. Sharma and Kumar gave the order of convergence using Taylor series expansions and derivatives up to the order <math>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 <mi>m</mi>\u0000 <mo>+</mo>\u0000 <mn>4</mn>\u0000 </mrow></math> that do not appear in the method. Hence, the applicability of it is very limited. The novelty of our article is that we use only the first derivative in our local convergence (that only appears on the proposed method). Error bounds and uniqueness results not given earlier are also provided based on q-continuity functions. We also work with Banach space instead of Euclidean space valued operators. This way the applicability of the solver is extended. Applications where the convergence criteria are tested to complete this article.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/cmm4.1184","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79103501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Numerical solution of nonlinear dual-phase-lag model for analyzing heat transfer in tissue during thermal therapy 热疗过程中组织传热非线性双相滞后模型的数值解

Computational and Mathematical Methods Pub Date : 2021-07-24 DOI: 10.1002/cmm4.1183

Neha Sharma, Surjan Singh, Dinesh Kumar

引用次数: 2

Conserving the European Bonelli's eagle in spatiotemporal domain: Lesson from its feeding pattern 在时空域中保护欧洲波内利鹰:从其摄食模式的教训

Computational and Mathematical Methods Pub Date : 2021-07-11 DOI: 10.1002/cmm4.1181

Ranjit Kumar Upadhyay

{"title":"Conserving the European Bonelli's eagle in spatiotemporal domain: Lesson from its feeding pattern","authors":"Ranjit Kumar Upadhyay","doi":"10.1002/cmm4.1181","DOIUrl":"10.1002/cmm4.1181","url":null,"abstract":"Bonelli's eagle (Hieraaetus fasciatus), a threatened species in Western Europe, has suffered a critical and severe decline in last two decades. In this article, a qualitative analysis of an ecoepidemiological model which consists of two prey and a predator is carried out. We proposed and designed a spatiotemporal model to predict the distribution of a territorial predator, Bonelli's eagle and its two main prey species (rabbit and red-legged partridge). Bounded positive solution, feasibility of the equilibria, and their stability analysis are determined for the nonspatial counterpart of the system. Criteria for diffusion-driven instability caused by local random movements of rabbits, partridges, and Bonelli's eagle are obtained. Possible implications of the result for Bonelli's eagle conservation are discussed. We show that the inclusion of second prey in the system can drastically change the dynamics from the single prey case. We also found that the presence of a second prey is beneficial for the conservation of the threatened Bonelli's eagle population in Europe. Results obtained from theoretical analysis of the nonspatial model agree very well with the numerical simulation results. Lastly, via numerical simulation, we illustrate the effect of diffusion of the dynamical system in the spatial/spatiotemporal domain by different pattern formations.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/cmm4.1181","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73465218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Modeling the role of information on the spread of online shopping 建模信息对网络购物传播的作用

Computational and Mathematical Methods Pub Date : 2021-07-11 DOI: 10.1002/cmm4.1182

Sandeep Sharma

{"title":"Modeling the role of information on the spread of online shopping","authors":"Sandeep Sharma","doi":"10.1002/cmm4.1182","DOIUrl":"10.1002/cmm4.1182","url":null,"abstract":"For at least the past 5 years, online shopping has witnessed exponential growth. The trend of online shopping is very much popular in current times. In particular, the young population frequently turned up to different online shopping sites for their routine purchase. The information or awareness created by online shoppers also plays a pivotal role in the growth of online shopping. People got attracted to online shopping when they heard about attractive offers, discounts, and other benefits of online shopping from someone on their social network. Moreover, online shopping sites also introduced the review and rating facilities for individual products listed on their web page or mobile applications. Online buyers also use the information provided by the reviews before finalizing the purchase of an item. Motivated by these facts, in this article, we propose a compartmental mathematical model to study the impact of information on the growth of online shopping. The model subsequently subjected to dynamical analysis using the tools of dynamical systems and the theory of differential equations. Numerical simulation has been performed to validate our analytical findings.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/cmm4.1182","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73535913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Extensions on a local convergence result by Dennis and Schnabel for Newton's method with applications Dennis和Schnabel对牛顿方法的一个局部收敛结果的推广及其应用

Computational and Mathematical Methods Pub Date : 2021-06-27 DOI: 10.1002/cmm4.1179

Ioannis K. Argyros, Michael Argyros, Johan Ceballos, Mariana Ceballos, Daniel González

引用次数: 0

On the Sitnikov-like N-body problem with quasi-homogeneous potential 拟齐次势的Sitnikov-like N-body问题

Computational and Mathematical Methods Pub Date : 2021-06-27 DOI: 10.1002/cmm4.1180

Md Sanam Suraj, Rajiv Aggarwal, Vipin Kumar Aggarwal, Md Chand Asique, Amit Mittal

{"title":"On the Sitnikov-like N-body problem with quasi-homogeneous potential","authors":"Md Sanam Suraj, Rajiv Aggarwal, Vipin Kumar Aggarwal, Md Chand Asique, Amit Mittal","doi":"10.1002/cmm4.1180","DOIUrl":"10.1002/cmm4.1180","url":null,"abstract":"In the present article, the periodic solutions of the N-body with quasi-homogeneous potential in the Sitnikov sense by applying the multiple methods of scale (MMS) and Lindstedt–Poincaré (LP) technique are obtained. However, these methods are used to find the approximate periodic solutions in the closed form by eliminating the secular terms. In addition of the Newtonian potential and forces, we consider that the big bodies create quasi-homogeneous potentials. We add the inverse cubic corrective term to the inverse square Newtonian law of gravitation, in order to approximate the various phenomena due to the shape of the bodies or the radiation emitting from them. We study the Sitnikov motion in the N-bodies under this consideration. We, further, analyzed the obtain approximate periodic solutions of the Sitnikov motion, for <math>\u0000 <mrow>\u0000 <mi>ν</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mn>7</mn>\u0000 </mrow></math> by using the MMS and LP-method, in closed form. The numerical comparisons are presented in the first and second approximated solutions obtained by using MMS and numerical solutions obtained by LP-method are illustrated graphically. The effect of initial conditions on the solutions of the Sitnikov motion is illustrated graphically obtained by both the techniques. It is observed that the choice of initial conditions plays a crucial role in the numerical and approximate solutions.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/cmm4.1180","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86684531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

A hybrid numerical scheme for singularly perturbed parabolic differential-difference equations arising in the modeling of neuronal variability 神经元变异性建模中奇异摄动抛物型微分-差分方程的混合数值格式

Computational and Mathematical Methods Pub Date : 2021-06-25 DOI: 10.1002/cmm4.1178

Imiru Takele Daba, Gemechis File Duressa

{"title":"A hybrid numerical scheme for singularly perturbed parabolic differential-difference equations arising in the modeling of neuronal variability","authors":"Imiru Takele Daba, Gemechis File Duressa","doi":"10.1002/cmm4.1178","DOIUrl":"10.1002/cmm4.1178","url":null,"abstract":"This study aims at constructing a robust numerical scheme for solving singularly perturbed parabolic delay differential equations arising in the modeling of neuronal variability. Taylor's series expansion is applied to approximate the shift terms. The obtained result is approximated by using the implicit Euler method in the temporal discretization on a uniform step size with the hybrid numerical scheme consisting of the midpoint upwind method in the outer layer region and the cubic spline in tension method in the inner layer region on a piecewise uniform Shishkin mesh in the spatial discretization. The constructed scheme is shown to be an <math>\u0000 <mrow>\u0000 <mi>ε</mi>\u0000 </mrow></math>-uniformly convergent accuracy of order <math>\u0000 <mrow>\u0000 <mi>O</mi>\u0000 <mfenced>\u0000 <mrow>\u0000 <mi>Λ</mi>\u0000 <mi>t</mi>\u0000 <mo>+</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ln</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow></math>. Two model examples are given to testify the theoretical findings.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/cmm4.1178","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80126580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

A linearized spectral collocation method for Riesz space fractional nonlinear reaction–diffusion equations Riesz空间分数阶非线性反应扩散方程的线性化谱配置方法

Computational and Mathematical Methods Pub Date : 2021-05-31 DOI: 10.1002/cmm4.1177

Mustafa Almushaira

引用次数: 0

Two derivative-free algorithms for constrained nonlinear monotone equations 约束非线性单调方程的两种无导数算法

Computational and Mathematical Methods Pub Date : 2021-05-15 DOI: 10.1002/cmm4.1176

Auwal Bala Abubakar, Hassan Mohammad, Mohammed Yusuf Waziri

引用次数: 1

Some integral inequalities involving Mittag–Leffler functions for tgs-convex functions 关于tgs-凸函数的若干涉及Mittag-Leffler函数的积分不等式

Computational and Mathematical Methods Pub Date : 2021-05-12 DOI: 10.1002/cmm4.1175

Ghulam Farid, Moquddsa Zahra

引用次数: 2