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Numerical solution of stiff chemical reaction ODEs using implicit–explicit Runge–Kutta methods 用隐式-显式龙格-库塔方法求解刚性化学反应ode
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2026-10-13 DOI: 10.1007/s10910-026-01838-w
Lingxue Zhu, Wei Shi, Kai Liu
{"title":"Numerical solution of stiff chemical reaction ODEs using implicit–explicit Runge–Kutta methods","authors":"Lingxue Zhu,&nbsp;Wei Shi,&nbsp;Kai Liu","doi":"10.1007/s10910-026-01838-w","DOIUrl":"10.1007/s10910-026-01838-w","url":null,"abstract":"<div><p>Stiff ordinary differential equations frequently arise in chemical kinetics because reaction time scales can span many orders of magnitude. This work presents a systematic methodological and numerical study of high-order implicit–explicit Runge–Kutta schemes on the Akzo Nobel, Robertson, HIRES, and 20-species air-pollution benchmarks. For each problem, a reaction-based partition is specified and then assessed along a reference trajectory through the spectral radii of the full, implicit, and explicit Jacobians. Classical fixed-step RK4 and adaptive <span>ode45</span> are used to demonstrate the explicit stability restriction, while comparisons with the corresponding fourth- and fifth-order DIRK schemes, which share the same implicit tableaux, isolate the effect of the IMEX partition. In the reported tests, the IMEX schemes attain accuracy comparable to their matched DIRK counterparts at lower computational cost. Linear invariants are preserved to machine precision, whereas nonnegativity is not guaranteed and can be lost on coarse grids. These results clarify both the practical benefits and the limitations of high-order IMEX integration for stiff chemical kinetics.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189004","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
Structural characterization of stochastic detailed balance in chemical reaction networks 化学反应网络中随机精细平衡的结构表征
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2026-10-08 DOI: 10.1007/s10910-026-01840-2
Shangbin Ma, Youming Li
{"title":"Structural characterization of stochastic detailed balance in chemical reaction networks","authors":"Shangbin Ma,&nbsp;Youming Li","doi":"10.1007/s10910-026-01840-2","DOIUrl":"10.1007/s10910-026-01840-2","url":null,"abstract":"<div><p>The global potential of a chemical reaction network has many applications and is closely related to stochastic detailed balance. However, many fundamental questions concerning stochastic detailed balance remain unresolved, such as whether it depends on the system volume and how to construct new systems that satisfy it. In this paper, we show that stochastic detailed balance may depend on the system volume. We therefore introduce four types of stochastic detailed balance according to their dependence on volume and rate constants, and then systematically investigate the relationships among them. Our results distinguish detailed balance arising from particular choices of volume and parameters from those enforced by network structure, and identify conditions under which detailed balance at one volume extends to all volumes. We further obtain a class of networks satisfying stochastic detailed balance for every volume and every positive choice of rate constants, and construct new systems whose global potentials exhibit double-well structures.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132681","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 approximate estimation of the maximum instantaneous reaction rate at high enzyme concentrations for the general modifier mechanism 对一般改性剂机制在高酶浓度下的最大瞬时反应速率的近似估计
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2026-10-08 DOI: 10.1007/s10910-026-01837-x
P. F. Zhuk, S. O. Karakhim
{"title":"An approximate estimation of the maximum instantaneous reaction rate at high enzyme concentrations for the general modifier mechanism","authors":"P. F. Zhuk,&nbsp;S. O. Karakhim","doi":"10.1007/s10910-026-01837-x","DOIUrl":"10.1007/s10910-026-01837-x","url":null,"abstract":"<div><p>The initial rate method is commonly used to study the kinetics of reactions proceeding by a general modifier mechanism. Its application assumes that the total enzyme concentration (<i>E</i><sub>0</sub>) is small compared to the total substrate concentration (<i>S</i><sub>0</sub>). Under in vivo conditions, however, the enzyme concentration is usually comparable to the substrate concentration. In this study, therefore, the maximum instantaneous reaction rate has been proposed as an alternative to the initial rate; the values of these rates are practically identical under the condition <i>S</i><sub>0</sub> &gt;&gt; <i>E</i><sub>0</sub>. Accurate calculation of the maximum instantaneous rate requires solving a system of differential equations, which complicates the practical analysis of reaction kinetics. In this study, an approximate method for calculating this rate has been proposed, which consists in solving a seventh-degree algebraic equation. This method’s effectiveness has been demonstrated in examples for both low and high enzyme concentrations.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132604","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
Two-dimensional turing patterns in a CIMA reaction with flow 流动CIMA反应的二维图灵模式
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2026-10-08 DOI: 10.1007/s10910-026-01836-y
Lawrence Forbes, Reuben Allen, Heath Dimsey, Michael Brideson
{"title":"Two-dimensional turing patterns in a CIMA reaction with flow","authors":"Lawrence Forbes,&nbsp;Reuben Allen,&nbsp;Heath Dimsey,&nbsp;Michael Brideson","doi":"10.1007/s10910-026-01836-y","DOIUrl":"10.1007/s10910-026-01836-y","url":null,"abstract":"<div><p>The Lengyel–Epstein mathematical model for the CIMA chemical reaction is studied. The reaction is envisaged to occur in a rectangularly-shaped batch spatial reactor. In addition, flow terms have been added to the original model, as an approximation to exchange of reagents with those in a well-mixed reservoir. These novel flow terms are responsible for the creation of parameter zones in which three different equilibrium states may exist. We demonstrate that large-amplitude limit-cycle oscillations can occur, enclosing three equilibria. Turing bifurcations are studied in detail, and it is shown that two-dimensional spatial patterns of chemical concentration can occur, both as time-dependent transient configurations and also as stationary spatial patterns.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-026-01836-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132603","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
Spectral analysis of the path signless laplacian matrix with QSPR applications to bioactive polyphenols 路径无符号拉普拉斯矩阵的QSPR光谱分析在生物活性多酚中的应用
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2026-10-05 DOI: 10.1007/s10910-026-01839-9
S. R. Sahana, Sabitha D’Souza, Swati Nayak
{"title":"Spectral analysis of the path signless laplacian matrix with QSPR applications to bioactive polyphenols","authors":"S. R. Sahana,&nbsp;Sabitha D’Souza,&nbsp;Swati Nayak","doi":"10.1007/s10910-026-01839-9","DOIUrl":"10.1007/s10910-026-01839-9","url":null,"abstract":"<div><p>For a graph <span>(varOmega )</span> with vertex set <span>(V(varOmega )={v_1,v_2,ldots ,v_n})</span>, the path matrix <span>(P(varOmega ))</span> is defined by assigning to its (<i>h</i>, <i>l</i>)-entry the maximum number of vertex-disjoint paths between <span>(v_h)</span> and <span>(v_l)</span> whenever <span>(hne l)</span>, and zero otherwise. Based on this matrix, we study the path signless Laplacian matrix <span>(PSL(varOmega ))</span> and its associated spectral properties. In this paper, we establish several bounds for the path signless Laplacian energy <span>(PSLE(varOmega ))</span> and investigate the spectral behaviour of <span>(PSL(varOmega ))</span> under various graph operations, including <i>p</i>-splitting and <i>p</i>-duplicate graphs, together with certain other graph classes. For these graph constructions, we derive the characteristic polynomials, determine the corresponding eigenvalues, analyze the inertia, and compute the resulting path signless Laplacian energies. Furthermore, to demonstrate the applicability of the proposed spectral descriptor, a QSPR analysis of bioactive polyphenols is carried out using the path signless Laplacian energy. Linear regression models are developed to study the correlation between <span>(PSLE(varOmega ))</span> and several physicochemical properties, including molecular complexity, molecular weight, polar surface area, and boiling point. The obtained results reveal strong correlations, indicating that the path signless Laplacian energy serves as an effective molecular descriptor in chemical graph theory and QSPR modeling.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-026-01839-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132363","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
Quantum particle on an elliptical path 椭圆路径上的量子粒子
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2026-10-05 DOI: 10.1007/s10910-026-01841-1
Francisco M. Fernández
{"title":"Quantum particle on an elliptical path","authors":"Francisco M. Fernández","doi":"10.1007/s10910-026-01841-1","DOIUrl":"10.1007/s10910-026-01841-1","url":null,"abstract":"<div><p>The Schrödinger equation for a quantum particle on an elliptical path can be solved exactly. The eigenvalues are given by <span>(E_{n}=n^{2}E_{1}, n=0,pm 1,pm 2,ldots )</span>, exactly as in the case of a circular path. The perturbation series in terms of a properly defined shape parameter <span>(xi )</span> converges for all <span>(-1le xi &lt;1)</span>.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132367","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 Novel Yang transform homotopy perturbation approach with applications to the multi-dimensional time-fractional Caputo-Fabrizio diffusion equations 一种新的Yang变换同伦摄动方法及其在多维时间分数阶Caputo-Fabrizio扩散方程中的应用
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2026-09-26 DOI: 10.1007/s10910-026-01835-z
Amjad Shaikh, Swarupkumar Bhalke
{"title":"A Novel Yang transform homotopy perturbation approach with applications to the multi-dimensional time-fractional Caputo-Fabrizio diffusion equations","authors":"Amjad Shaikh,&nbsp;Swarupkumar Bhalke","doi":"10.1007/s10910-026-01835-z","DOIUrl":"10.1007/s10910-026-01835-z","url":null,"abstract":"<div><p>In this paper, we present a novel approach to obtain the approximate solution of the time-fractional diffusion equations, that is the Yang transform homotopy perturbation method (YTHPM). The fractional order is considered in the sense of the Caputo-Fabrizio fractional derivative. We develop the algorithm of the Yang transform homotopy perturbation method, which is the combined form of the Yang Transform and the homotopy perturbation method. This technique provides an infinite series solution that converges to the exact solution rapidly. We present the convergence and error analysis results. We provide the two-dimensional and three-dimensional plots to show the accuracy and applicability of the proposed approach. Moreover, we use a table to compare the approximate and exact solutions from the point of view of absolute error. The results obtained indicate strong potential and are well-suited for solving multi-dimensional diffusion equations with time-fractional derivative.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035359","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
Indirect derivative fast Padé transform applied to magnetic resonance spectroscopy 间接导数快速帕德帕变换在磁共振波谱学中的应用
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2026-09-24 DOI: 10.1007/s10910-026-01834-0
Dževad Belkić, Karen Belkić
{"title":"Indirect derivative fast Padé transform applied to magnetic resonance spectroscopy","authors":"Dževad Belkić,&nbsp;Karen Belkić","doi":"10.1007/s10910-026-01834-0","DOIUrl":"10.1007/s10910-026-01834-0","url":null,"abstract":"<div><p>This article is on lineshape profiles by indirect derivatives of spectra reconstructed from time signals or free induction decay (FID) data encoded by magnetic resonance spectroscopy (MRS). Only the nonparametric reconstructions (shape estimations) are performed using for the first time the indirect version of the derivative fast Padé transform (dFPT). Here, the frequency-dependent derivative operator is not applied straight to the spectrum of the precomputed nonderivative fast Padé transform (FPT). Rather, the derivative operator is applied to the frequency-dependent complex exponential harmonic variable in the starting MacLaurin expansion, generating therein a time power function (monomial). From this derivative-modified MacLaurin expansion, the FPT is constructed. Thus, the indirect dFPT can equivalently be conceived as the FPT which processes the so-called FID moments defined as the products of the time monomial and the FID. The time monomial leads to ill-conditioning by enhancing noise from encoded FIDs. It is shown that this problem is automatically solvable in the indirect dFPT without any regularizing optimization. Moreover, high concordance is recorded in the results from the indirect dFPT with a constant (static) or derivative-adapted (dynamic) apodizations or by ignoring both attenuations of the FID moments.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-026-01834-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035290","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
Hierarchical parameterization of fullerenes via vertex combinations 通过顶点组合的富勒烯分层参数化
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2026-09-18 DOI: 10.1007/s10910-026-01830-4
Shaoqing Li
{"title":"Hierarchical parameterization of fullerenes via vertex combinations","authors":"Shaoqing Li","doi":"10.1007/s10910-026-01830-4","DOIUrl":"10.1007/s10910-026-01830-4","url":null,"abstract":"<div><p>A fullerene graph can be embedded in a piecewise linear manifold in which each non-hexagonal ring corresponds to a cone vertex. Two or three adjacent cone vertices can be combined into a cluster that is excised from a parent cone, whose apex represents the corresponding parent vertex. These clusters exhibit intrinsic symmetries on the parent cone, enabling a systematic reduction of any fullerene to a simpler parent structure with a natural parameterization. The resulting parameters provide a structured geometric characterization of fullerene families, including tubular fullerenes, octahedral fullerenes, and other symmetric variants. This framework provides a unified geometric basis for analyzing fullerene structures and enables systematic geometric characterization studies.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148987132","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 novel predictor–corrector method for solving the Schrödinger equation and related problems 求解Schrödinger方程及相关问题的一种新的预测校正方法
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2026-09-16 DOI: 10.1007/s10910-026-01831-3
Theodore E. Simos
{"title":"A novel predictor–corrector method for solving the Schrödinger equation and related problems","authors":"Theodore E. Simos","doi":"10.1007/s10910-026-01831-3","DOIUrl":"10.1007/s10910-026-01831-3","url":null,"abstract":"<div><p>We introduce a high-order predictor–corrector multistep method designed for oscillatory initial-value problems, including Schrödinger-type systems. The proposed scheme is constructed by enforcing exactness for a prescribed set of basis functions, consisting of polynomial terms together with trigonometric functions generated from a user-specified frequency parameter. This fitted construction aims to improve phase and amplitude behavior relative to standard constant-coefficient predictor–corrector variants. The stability of the resulting method is investigated by transforming the two-step iteration into an equivalent scalar recurrence and analyzing the location of the corresponding characteristic roots. Numerical experiments for Schrödinger-type coupled systems from quantum-chemistry applications and for representative oscillatory test problems confirm that the frequency-aware design yields improved long-time accuracy and reduced distortion.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148965460","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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