Computational and Mathematical Methods最新文献_第6页

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

Scale-deviating operators of Riesz type and the spaces of variable dimensions Riesz型尺度偏差算子和变维空间

Computational and Mathematical Methods Pub Date : 2021-05-08 DOI: 10.1002/cmm4.1174

Vladimir Kobelev

{"title":"Scale-deviating operators of Riesz type and the spaces of variable dimensions","authors":"Vladimir Kobelev","doi":"10.1002/cmm4.1174","DOIUrl":"10.1002/cmm4.1174","url":null,"abstract":"The article introduces the scale-deviating operator. The scale-deviating differential operator comprises the parameters to designate the operator order and the parameters to define the dimension of space. The operator order depends on the characteristic length κ. There are two types of linear scale-deviating operators. For the distances r, which are much less than κ, the scale-deviating operator of the first type <math>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 </mrow></math> reduces to the common operators. For the distances, which exceed the length κ, this operator reduces to the fractional Riesz operator. The second type of the scale-deviating operator <math>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 </mrow></math> behaves oppositely. For the distances r, which are much higher than κ, the scale-deviating operator of the second type reduces to the common operators. Finally, for the distances, which below the length κ, this operator lessens to the fractional Riesz operator. These linear, isotropic operators possess the order, less than two. The solutions of new scale-deviating equations and the shell theorem for these operators are provided closed form.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/cmm4.1174","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83769274","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

A class of weighted Hill estimators 一类加权Hill估计量

Computational and Mathematical Methods Pub Date : 2021-04-13 DOI: 10.1002/cmm4.1167

Frederico Caeiro, Ayana Mateus, Louiza Soltane

引用次数: 2

Numerical solution of third-order boundary value problems by using a two-step hybrid block method with a fourth derivative 用带四阶导数的两步混合块法数值解三阶边值问题

Computational and Mathematical Methods Pub Date : 2021-04-11 DOI: 10.1002/cmm4.1166

Mufutau Ajani Rufai, Higinio Ramos

引用次数: 2

Solving fully randomized higher-order linear control differential equations: Application to study the dynamics of an oscillator 求解完全随机化高阶线性控制微分方程:在振荡器动力学研究中的应用

Computational and Mathematical Methods Pub Date : 2021-04-06 DOI: 10.1002/cmm4.1163

Juan-Carlos Cortés, Ana Navarro-Quiles, José-Vicente Romero, María-Dolores Roselló

引用次数: 1

Efficiency of using adaptive artificial boundary conditions at computer simulation of contrast spatio-temporal laser-induced structures in a semiconductor 自适应人工边界条件在半导体激光诱导时空结构计算机模拟中的有效性

Computational and Mathematical Methods Pub Date : 2021-04-04 DOI: 10.1002/cmm4.1165

Vyacheslav Trofimov, Maria Loginova, Vladimir Egorenkov

{"title":"Efficiency of using adaptive artificial boundary conditions at computer simulation of contrast spatio-temporal laser-induced structures in a semiconductor","authors":"Vyacheslav Trofimov, Maria Loginova, Vladimir Egorenkov","doi":"10.1002/cmm4.1165","DOIUrl":"10.1002/cmm4.1165","url":null,"abstract":"Many problems of modern laser physics are governed by equations or sets of equations in an unbounded domain. For solving these problems using the computer simulation, it is necessary to introduce the bounded domain, which size should be extended significantly to avoid the spurious wave reflection from the domain boundaries. Alternatively, the artificial (non-reflective or transparent) boundary conditions should be stated. This approach is also effective for enhancing computation performance at the numerical solution of the nonlinear partial differential equations (PDEs). In the current paper, we investigate the laser pulse propagation in a semiconductor, governed by the Schrödinger equation, under the appearance of spatio-temporal contrast structures of semiconductor characteristics. Their evolution is described by a set of PDEs. The optical pulse is partly reflected from the boundaries of these structures. Consequently, even a little reflection of the optical pulse from the artificial boundaries can essentially distort the numerical solution. Thus, these artificial boundary conditions must possess a high quality to minimize their reflection coefficients. With this aim, we propose the method for constructing adaptive artificial boundary conditions and discuss their advantages.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/cmm4.1165","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74488255","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: 2