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On the Raleigh–Ritz variational method. Non-orthogonal basis set 关于 Raleigh-Ritz 变分法。非正交基集
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-06-28 DOI: 10.1007/s10910-024-01644-2
Francisco M. Fernández
{"title":"On the Raleigh–Ritz variational method. Non-orthogonal basis set","authors":"Francisco M. Fernández","doi":"10.1007/s10910-024-01644-2","DOIUrl":"https://doi.org/10.1007/s10910-024-01644-2","url":null,"abstract":"<p>We overview the main equations of the Rayleigh–Ritz variational method and discuss their connection with the problem of simultaneous diagonalization of two Hermitian matrices.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A fourth-order compact ADI scheme for solving a two-dimensional time-fractional reaction-subdiffusion equation 求解二维时间分数反应-次扩散方程的四阶紧凑 ADI 方案
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-06-25 DOI: 10.1007/s10910-024-01638-0
Pradip Roul, Vikas Rohil
{"title":"A fourth-order compact ADI scheme for solving a two-dimensional time-fractional reaction-subdiffusion equation","authors":"Pradip Roul, Vikas Rohil","doi":"10.1007/s10910-024-01638-0","DOIUrl":"https://doi.org/10.1007/s10910-024-01638-0","url":null,"abstract":"<p>This article aims at developing a computational scheme for solving the time fractional reaction-subdiffusion (TFRSD) equation in two space dimensions. The Caputo fractional derivative is used to describe the time-fractional derivative appearing in the problem and it is approximated by using the <i>L</i>1 scheme. A compact difference scheme of order four is utilized for discretization of the spatial derivatives. Some test problems are solved to investigate the accuracy of the scheme. The computed results confirm that the scheme has convergence of order four in space and an order of <span>({min {{2-alpha ,1+alpha }}})</span> in the time direction, where <span>(alpha in (0,1))</span> is the order of fractional derivative. Moreover, the computed results are compared with those obtained by other methods in order to justify the advantage of proposed algorithm.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Convergence analysis of optimal iterative family for multiple roots and its applications 多根最优迭代族的收敛性分析及其应用
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-06-24 DOI: 10.1007/s10910-024-01640-6
Bhavna, Saurabh Bhatia
{"title":"Convergence analysis of optimal iterative family for multiple roots and its applications","authors":"Bhavna, Saurabh Bhatia","doi":"10.1007/s10910-024-01640-6","DOIUrl":"https://doi.org/10.1007/s10910-024-01640-6","url":null,"abstract":"<p>In this paper, we use weight function approach to construct a new King-like family of methods to solve nonlinear equations with multiple roots. Here the weight functions are chosen appropriately to reach the maximum convergence order eight and the family is optimal in the sense of Kung–Traub conjecture. Moreover, local convergence of a fourth order modified King’s family for multiple roots is also studied. Radii of convergence balls of fourth order schemes are computed and compared with an existing method. Numerical examples have been presented based on applications of some real life problems and the results obtained show the superiority of our eighth order schemes over the existing ones. To study the dynamical behaviour of the proposed schemes, basins of attraction have also been presented which verifies that proposed eighth order schemes have more convergent points and requires less number of iterations in comparison to the existing methods.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Graph realization of sets of integers 整数集合的图形实现
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-06-24 DOI: 10.1007/s10910-024-01642-4
Piotr Wawrzyniak, Piotr Formanowicz
{"title":"Graph realization of sets of integers","authors":"Piotr Wawrzyniak, Piotr Formanowicz","doi":"10.1007/s10910-024-01642-4","DOIUrl":"https://doi.org/10.1007/s10910-024-01642-4","url":null,"abstract":"<p>Graph theory is used in many areas of chemical sciences, especially in molecular chemistry. It is particularly useful in the structural analysis of chemical compounds and in modeling chemical reactions. One of its applications concerns determining the structural formula of a chemical compound. This can be modeled as a variant of the well-known graph realization problem. In the classical version of the problem, a sequence of natural numbers is given, and the question is whether there exists a graph in which the vertices have degrees equal to the given numbers. In the variant considered in this paper, instead of a sequence of natural numbers, a sequence of sets of natural numbers is given, and the question is whether there exists a multigraph such that each of its vertices has a degree equal to a number from one of the sets. This variant of the graph realization problem matches the nature of the problem of determining the structural formula of a chemical compound better than other variants considered in the literature. We propose a polynomial time exact algorithm solving this variant of the problem.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A parameter-uniform hybrid scheme designed for multi-point boundary value problems that are perturbed 为受扰动的多点边界值问题设计的参数统一混合方案
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-06-24 DOI: 10.1007/s10910-024-01639-z
Parvin Kumari, Devendra Kumar, Jesus Vigo-Aguiar
{"title":"A parameter-uniform hybrid scheme designed for multi-point boundary value problems that are perturbed","authors":"Parvin Kumari, Devendra Kumar, Jesus Vigo-Aguiar","doi":"10.1007/s10910-024-01639-z","DOIUrl":"https://doi.org/10.1007/s10910-024-01639-z","url":null,"abstract":"<p>The numerical solution of a class of second-order singularly perturbed three-point boundary value problems (BVPs) in 1D is achieved using a uniformly convergent, stable, and efficient difference method on a piecewise-uniform mesh. The presence of a boundary layer(s) on one (or both) of the interval’s endpoints is caused by the presence of the tiny parameter in the highest order derivative. As the perturbation parameter approaches 0, traditional numerical techniques on the uniform mesh become insufficient, resulting in poor accuracy and large blows without the use of an excessive number of points. Specially customised techniques, such as fitted operator methods or methods linked to adapted or fitted meshes that solve essential characteristics such as boundary and/or inner layers, are necessary to overcome this drawback. We developed a fitted-mesh technique in this paper that works for all perturbation parameter values. The monotone hybrid technique, which includes midway upwinding in the outer area and centre differencing in the layer region on a fitted-mesh condensing in the border layer region, is the basis for our difference scheme. In a discrete <span>(L^infty )</span> norm, uniform error estimates are constructed, and the technique is demonstrated to be parameter-uniform convergent of order two (up to a logarithmic factor). To show the effectiveness of the recommended technique and to corroborate the theoretical findings, a numerical example is presented. In practise, the convergence obtained matches the theoretical expectations.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Linearized Boltzmann collision operator for a mixture of monatomic and polyatomic chemically reacting species 单原子和多原子化学反应混合物的线性化玻尔兹曼碰撞算子
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-06-19 DOI: 10.1007/s10910-024-01633-5
Niclas Bernhoff
{"title":"Linearized Boltzmann collision operator for a mixture of monatomic and polyatomic chemically reacting species","authors":"Niclas Bernhoff","doi":"10.1007/s10910-024-01633-5","DOIUrl":"https://doi.org/10.1007/s10910-024-01633-5","url":null,"abstract":"<p>At higher altitudes near space shuttles moving at hypersonic speed the air is excited to high temperatures. Then not only mechanical collisions are affecting the gas flow, but also chemical reactions have an impact on such hypersonic flows. In this work we insert chemical reactions, in form of dissociations and associations, in a model for a mixture of mono- and polyatomic (non-reacting) species. More general chemical reactions, e.g., bimolecular ones, can be obtained by instant combinations of the considered reactions. Polyatomicity is here modelled by a continuous internal energy variable and the evolution of the gas is described by a Boltzmann equation. In the Chapman-Enskog process—and related half-space problems—the linearized Boltzmann collision operator plays a central role. Here we extend some important properties of the linearized operator to the considered model with chemical reactions. A compactness result, that the linearized operator can be decomposed into a sum of a positive multiplication operator—the collision frequency—and a compact integral operator, is obtained. The terms of the integral operator are shown to be (at least) uniform limits of Hilbert-Schmidt integral operators and, thereby, compact operators. Self-adjointness of the linearized operator follows as a direct consequence. Also, bounds on—including coercivity of—the collision frequency is obtained for hard sphere, as well as hard potentials with cutoff, like models. As consequence, Fredholmness as well as the domain of the linearized operator are obtained.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Numerical investigation of two fractional operators for time fractional delay differential equation 时间分数延迟微分方程两个分数算子的数值研究
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-06-19 DOI: 10.1007/s10910-024-01637-1
Reetika Chawla, Devendra Kumar, Dumitru Baleanu
{"title":"Numerical investigation of two fractional operators for time fractional delay differential equation","authors":"Reetika Chawla, Devendra Kumar, Dumitru Baleanu","doi":"10.1007/s10910-024-01637-1","DOIUrl":"https://doi.org/10.1007/s10910-024-01637-1","url":null,"abstract":"<p>This article compared two high-order numerical schemes for convection-diffusion delay differential equation via two fractional operators with singular kernels. The objective is to present two effective schemes that give <span>((3-alpha ))</span> and second order of accuracy in the time direction when <span>(alpha in (0,1))</span> using Caputo and Modified Atangana-Baleanu Caputo derivatives, respectively. We also implemented a trigonometric spline technique in the space direction, giving second order of accuracy. Moreover, meticulous analysis shows these numerical schemes to be unconditionally stable and convergent. The efficiency and reliability of these schemes are illustrated by numerical experiments. The tabulated results obtained from test examples have also shown the comparison of these operators.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamical behavior of a classical stochastic delayed chemostat model 经典随机延迟恒温模型的动力学行为
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-06-14 DOI: 10.1007/s10910-024-01632-6
Xiaofeng Zhang, Shulin Sun
{"title":"Dynamical behavior of a classical stochastic delayed chemostat model","authors":"Xiaofeng Zhang, Shulin Sun","doi":"10.1007/s10910-024-01632-6","DOIUrl":"https://doi.org/10.1007/s10910-024-01632-6","url":null,"abstract":"","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141344297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analysis of an almost second-order parameter-robust numerical technique for a weakly coupled system of singularly perturbed convection-diffusion equations 奇异扰动对流扩散方程弱耦合系统的近二阶参数稳健数值技术分析
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-06-12 DOI: 10.1007/s10910-024-01634-4
S. C. S. Rao, V. Srivastava
{"title":"Analysis of an almost second-order parameter-robust numerical technique for a weakly coupled system of singularly perturbed convection-diffusion equations","authors":"S. C. S. Rao, V. Srivastava","doi":"10.1007/s10910-024-01634-4","DOIUrl":"https://doi.org/10.1007/s10910-024-01634-4","url":null,"abstract":"","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141353328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An effective multistep fourteenth-order phase-fitting approach to solving chemistry problems 解决化学问题的有效多步十四阶相位拟合方法
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-06-12 DOI: 10.1007/s10910-024-01628-2
Hui Huang, Cheng Liu, Chia-Liang Lin, T. E. Simos
{"title":"An effective multistep fourteenth-order phase-fitting approach to solving chemistry problems","authors":"Hui Huang, Cheng Liu, Chia-Liang Lin, T. E. Simos","doi":"10.1007/s10910-024-01628-2","DOIUrl":"https://doi.org/10.1007/s10910-024-01628-2","url":null,"abstract":"","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141353321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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