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Superfast computational approach using wavelets for nonlinear elliptic PDEs 非线性椭圆偏微分方程的小波超快速计算方法
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-12-11 DOI: 10.1007/s10910-025-01760-7
Vivek Kumar, Manoj Kumar
{"title":"Superfast computational approach using wavelets for nonlinear elliptic PDEs","authors":"Vivek Kumar,&nbsp;Manoj Kumar","doi":"10.1007/s10910-025-01760-7","DOIUrl":"10.1007/s10910-025-01760-7","url":null,"abstract":"<div><p>This study presents a unified numerical strategy that eliminates higher-order partial derivatives by employing Genocchi wavelets, their operational matrix of integration, and the collocation method for derivative terms. This approach serves as an alternative to traditional iterative methods, which often struggle to handle highly nonlinear problems effectively. The analysis and numerical solution of elliptic partial differential equations are discussed within the framework of the Genocchi Wavelet Collocation Method (GWCM). In this study, we examine the convergence, error estimation, and rapid applicability of the proposed method to a diverse range of problems. The effectiveness of the approach is demonstrated through detailed numerical experiments, with results presented in both tabular and graphical formats for clear comparison. The findings confirm the superior performance of GWCM over traditional methods, particularly under various parameter variations. One of the key advantages of this method is its ease of implementation and computational efficiency. The obtained solutions closely match the exact solutions, and an interesting observation is that for elliptic differential equations with polynomial solutions of finite degree, the method produces zero error. All computations are carried out using the latest version of MATLAB, ensuring accuracy and reliability.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145719265","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 high-accuracy (L2text {-}1_{sigma }) approach for time-fractional diffusion equations on non-uniform mesh 非均匀网格上时间分数扩散方程的高精度(L2text {-}1_{sigma })方法
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-11-07 DOI: 10.1007/s10910-025-01752-7
Pradip Roul, Vikas Kumar
{"title":"A high-accuracy (L2text {-}1_{sigma }) approach for time-fractional diffusion equations on non-uniform mesh","authors":"Pradip Roul,&nbsp;Vikas Kumar","doi":"10.1007/s10910-025-01752-7","DOIUrl":"10.1007/s10910-025-01752-7","url":null,"abstract":"<div><p>The authors of Roul et al. (J Math Chem 61:2146–2175, 2023) developed a numerical method for the time-fractional diffusion equation. In this method, the <i>L</i>1 scheme is employed on a uniform mesh for time discretization and a compact finite difference scheme for spatial discretization. They have ignored the initial weak singularity at <span>(t=0)</span>. The present study applies the <span>(L2text {-}1_{sigma })</span> scheme on a graded temporal mesh, providing an improvement over the <i>L</i>1 scheme by accurately approximating the Caputo time-fractional derivative and capturing the initial-time singularity. Spatial derivatives are approximated using a high-order compact finite difference scheme. The stability and convergence of the proposed scheme are rigorously proven using the energy method, in contrast to the Von-Neumann analysis used in Roul et al. (J Math Chem 61:2146–2175, 2023), which is limited to periodic and homogeneous boundary conditions. The proposed scheme achieves a temporal accuracy of <span>(min {ralpha ,,2})</span>, with <span>(alpha in (0,1))</span>, and fourth-order spatial accuracy. Numerical experiments validate the theoretical findings, and comparisons with Roul et al. (J Math Chem 61:2146–2175, 2023) and Roul (J Comput Appl Math 451:116033,2024) demonstrate the superior accuracy of the proposed approach.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 10","pages":"2167 - 2196"},"PeriodicalIF":2.0,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145510687","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
Revisiting analysis for Michaelis-Menten kinetics and a non-standard finite-difference-method for its discretization Michaelis-Menten动力学的重新分析及其离散化的非标准有限差分法
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-11-04 DOI: 10.1007/s10910-025-01755-4
Benjamin Wacker
{"title":"Revisiting analysis for Michaelis-Menten kinetics and a non-standard finite-difference-method for its discretization","authors":"Benjamin Wacker","doi":"10.1007/s10910-025-01755-4","DOIUrl":"10.1007/s10910-025-01755-4","url":null,"abstract":"<div><p>In this work, we reconsider the classical, non-linear set of ordinary differential equations for Michaelis-Menten kinetics of enzyme reactions. As the first contribution, we prove non-negativity, boundedness by two conservation properties, existence and uniqueness globally in time of solutions to this time-continuous model. As the second contribution, we show that the unique equilibrium state is globally asymptotically stable by application of LaSalle’s invariance principle through a suitable Lyapunov function. As the third and main contribution, we introduce a non-standard finite-difference-method based on the implicit Eulerian time-stepping method for the discretization of the time-continuous dynamical system. We reformulate its numerical solution algorithm by an explicit scheme and demonstrate that all desirable properties of the time-continuous model transfer to the proposed time-discrete variant. Finally, we highlight the theoretical findings by numerical experiments.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 10","pages":"2138 - 2166"},"PeriodicalIF":2.0,"publicationDate":"2025-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-025-01755-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145510456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On h-integral Sombor indices: theory and chemical applications 关于h积分Sombor指标：理论与化学应用
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-10-27 DOI: 10.1007/s10910-025-01758-1
Jorge Batanero, Edil D. Molina, José M. Rodríguez, José M. Sigarreta
{"title":"On h-integral Sombor indices: theory and chemical applications","authors":"Jorge Batanero,&nbsp;Edil D. Molina,&nbsp;José M. Rodríguez,&nbsp;José M. Sigarreta","doi":"10.1007/s10910-025-01758-1","DOIUrl":"10.1007/s10910-025-01758-1","url":null,"abstract":"<div><p>Topological indices play a crucial role in the prediction of physicochemical and biological properties of molecules. Recently, Ivan Gutman introduced the Sombor index, a new vertex-degree-based topological index that possesses significant geometric meaning. Since its introduction, this index has garnered substantial attention in mathematical chemistry and graph theory, leading to a surge in research exploring its properties, applications, and extensions. Motivated by its geometric foundation, we investigate in this paper various generalizations of the integral Sombor indices, analyzing their structural characteristics and mathematical implications. In addition, we study the applications of these indices in modeling the entropy of octane isomers.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 10","pages":"2111 - 2137"},"PeriodicalIF":2.0,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145510887","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
Stability of biochemical reaction networks with general kinetics and distributed time delays 具有一般动力学和分布时滞的生化反应网络的稳定性
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-10-23 DOI: 10.1007/s10910-025-01756-3
Gyula Molnár, Mihály A. Vághy, Gábor Szederkényi
{"title":"Stability of biochemical reaction networks with general kinetics and distributed time delays","authors":"Gyula Molnár,&nbsp;Mihály A. Vághy,&nbsp;Gábor Szederkényi","doi":"10.1007/s10910-025-01756-3","DOIUrl":"10.1007/s10910-025-01756-3","url":null,"abstract":"<div><p>Distributed delays play an important role in biological modeling, and are often inevitable to obtain a sufficiently precise quantitative description of certain important processes. It is known from previous studies that mass-action type complex balanced chemical reaction networks (CRNs) containing distributed delays are stable. In this paper, we consider complex balanced biochemical reaction networks with distributed delays, containing a general class of reaction rates including Michaelis–Menten and Hill-type kinetics. We show that for integrable delay distributions defined on a finite time interval, there exists precisely one equilibrium in each stoichiometric compatibility class. The local stability of the equilibria is shown using a logarithmic Lyapunov–Krasovski functional. The theoretical results are demonstrated through two illustrative examples.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 10","pages":"2088 - 2110"},"PeriodicalIF":2.0,"publicationDate":"2025-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-025-01756-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145510946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Gutman-Milovanović index in Mathematical Chemistry 数学化学中的古特曼-米洛瓦诺维奇指数
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-10-17 DOI: 10.1007/s10910-025-01753-6
Ana Portilla, José M. Rodríguez, Isabel Salas Lorenzo, José M. Sigarreta
{"title":"The Gutman-Milovanović index in Mathematical Chemistry","authors":"Ana Portilla,&nbsp;José M. Rodríguez,&nbsp;Isabel Salas Lorenzo,&nbsp;José M. Sigarreta","doi":"10.1007/s10910-025-01753-6","DOIUrl":"10.1007/s10910-025-01753-6","url":null,"abstract":"<div><p>One of the most important pieces of information related to molecular graphs is the determination (when possible) of upper and lower bounds for their corresponding topological indices. Such bounds make it possible to establish the approximate range of the topological indices in terms of molecular structural parameters. The purpose of this paper is to provide new inequalities for the Gutman-Milovanović index, which generalizes important indices such as the general second Zagreb index and the general sum-connectivity index. Moreover, the characterization of extremal graphs with respect to many of these inequalities is obtained. It is a well-known fact that the main application of topological indices is focused on understanding the physicochemical properties of chemical compounds; nevertheless, some additional applications are given to the study of the physicochemical properties of octane isomers. These are compounds that are especially relevant in the chemical and petroleum industries, but are also beginning to be used in the pharmaceutical industry.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 10","pages":"2068 - 2087"},"PeriodicalIF":2.0,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145511055","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
Bounds for the elliptic sombor index and applications 椭圆sombor指数的界及其应用
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-10-16 DOI: 10.1007/s10910-025-01757-2
Ana Granados, Edil D. Molina, Yamilet Quintana, Eva Tourís
{"title":"Bounds for the elliptic sombor index and applications","authors":"Ana Granados,&nbsp;Edil D. Molina,&nbsp;Yamilet Quintana,&nbsp;Eva Tourís","doi":"10.1007/s10910-025-01757-2","DOIUrl":"10.1007/s10910-025-01757-2","url":null,"abstract":"<div><p>In this paper, the elliptic Sombor index is studied and new upper and lower bounds for it are established. These bounds involve terms related to the <span>(alpha )</span>-Sombor index, the symmetric division deg index, the Gutman–Milovanović index, the general sum-connectivity index, and the hyperbolicity constant. Also, physicochemical properties of polyaromatic hydrocarbons using the elliptic Sombor index are modeled.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 10","pages":"2051 - 2067"},"PeriodicalIF":2.0,"publicationDate":"2025-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145510791","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
Correction: Spectral polynomials, graph descriptors, spectra, and entropies of cage graphs 修正：谱多项式，图描述符，谱，和笼图的熵
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-10-15 DOI: 10.1007/s10910-025-01751-8
Krishnan Balasubramanian
{"title":"Correction: Spectral polynomials, graph descriptors, spectra, and entropies of cage graphs","authors":"Krishnan Balasubramanian","doi":"10.1007/s10910-025-01751-8","DOIUrl":"10.1007/s10910-025-01751-8","url":null,"abstract":"","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 9","pages":"1989 - 1992"},"PeriodicalIF":2.0,"publicationDate":"2025-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145341374","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
Superconvergence analysis of symmetric Gauss-type exponential collocation integrators for solving the multidimensional nonlinear first-order partial differential equations 对称高斯型指数配置积分器解多维非线性一阶偏微分方程的超收敛分析
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-10-13 DOI: 10.1007/s10910-025-01754-5
Xiumei Wu, Yonglei Fang, Changying Liu, Yuanling Song
{"title":"Superconvergence analysis of symmetric Gauss-type exponential collocation integrators for solving the multidimensional nonlinear first-order partial differential equations","authors":"Xiumei Wu,&nbsp;Yonglei Fang,&nbsp;Changying Liu,&nbsp;Yuanling Song","doi":"10.1007/s10910-025-01754-5","DOIUrl":"10.1007/s10910-025-01754-5","url":null,"abstract":"<div><p>The main objective of this research is to develop and analyze high-order symmetric Gauss-type exponential collocation time-stepping methods for solving systems of nonlinear first-order partial differential equations (PDEs). Initially, the nonlinear PDEs are reformulated as an abstract Hamiltonian ordinary differential equation (ODE) system in an appropriate infinite-dimensional function space. Subsequently, the Gauss-type exponential collocation time integrators are derived. The symmetry, local error bounds and nonlinear stability of the proposed time integrators are rigorously analysed in details. Furthermore, the rigourous convergence analysis demonstrates that Gauss-type exponential collocation time integrators can achieve superconvergence. Numerical experiments verify our theoretical analysis results, and demonstrate the remarkable superiority in comparison with the traditional temporal integration methods.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 10","pages":"2023 - 2050"},"PeriodicalIF":2.0,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145511027","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
Efficient low-order Adams–Bashforth–Moulton trigonometrically-fitted methods 高效的低阶Adams-Bashforth-Moulton三角拟合方法
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-09-18 DOI: 10.1007/s10910-025-01748-3
Marina A. Medvedeva, Theodore E. Simos
{"title":"Efficient low-order Adams–Bashforth–Moulton trigonometrically-fitted methods","authors":"Marina A. Medvedeva,&nbsp;Theodore E. Simos","doi":"10.1007/s10910-025-01748-3","DOIUrl":"10.1007/s10910-025-01748-3","url":null,"abstract":"<div><p>This study presents a novel low-order Adams–Bashforth–Moulton predictor–corrector algorithm. This new approach was able to incorporate any linear combination of the functions <span>(left[ 1, , x, , x^2, , e^{I, v , x} right] )</span>. Stability zones are established for the novel approach. Using cases from chemistry and other fields, we test how well the recently suggested technique works.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 9","pages":"2001 - 2022"},"PeriodicalIF":2.0,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145341176","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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