Journal of Computational and Applied Mathematics最新文献

{"title":"A multiple-dynamics-preserving splitting mixed finite element method for 2D time-fractional molecular beam epitaxy model with slope selection","authors":"Wanqiu Yuan,&nbsp;Chengjian Zhang","doi":"10.1016/j.cam.2025.117137","DOIUrl":"10.1016/j.cam.2025.117137","url":null,"abstract":"<div><div>This paper deals with a new numerical method and its discrete dynamical analysis for 2D time-fractional molecular beam epitaxy model with slope selection. A multiple-dynamics-preserving splitting mixed finite element method is proposed to solve the model. A unique solvability criterion of the method is given. Under no stepsize constraint, the method is proved to be energy-stability-preserving, variational-energy-dissipation-law-preserving and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm-stability-preserving in the discrete sense. Moreover, an error estimate of the method is derived under the suitable condition, which shows that the method can arrive at convergence order <span><math><mrow><mn>2</mn><mo>−</mo><mi>α</mi></mrow></math></span> (resp. <span><math><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow></math></span>) in time (resp. in space), where <span><math><mi>α</mi></math></span> and <span><math><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow></math></span> denote the order of fractional derivatives in the model and the dimension of the used finite element space, respectively. By performing a series of numerical experiments, the error estimate and discrete dynamical properties of the method are further confirmed.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117137"},"PeriodicalIF":2.6,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the stability of IMEX BDF methods for DDEs and PDDEs","authors":"Ana Tercero-Báez ,&nbsp;Jesús Martín-Vaquero","doi":"10.1016/j.cam.2025.117044","DOIUrl":"10.1016/j.cam.2025.117044","url":null,"abstract":"<div><div>In this paper, the stability of IMEX-BDF methods for delay differential equations (DDEs) is studied based on the test equation <span><math><mrow><msup><mrow><mi>y</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mi>A</mi><mi>y</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><mi>B</mi><mi>y</mi><mrow><mo>(</mo><mi>t</mi><mo>−</mo><mi>τ</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>τ</mi></math></span> is a constant delay, <span><math><mi>A</mi></math></span> diagonalizes in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>, but <span><math><mi>B</mi></math></span> might be any matrix. First, it is analyzed the case where both matrices diagonalize simultaneously, and sufficient conditions to obtain linear stability are proved. However, the paper focuses on the case where the matrices <span><math><mi>A</mi></math></span> and <span><math><mi>B</mi></math></span> are not simultaneously diagonalizable. The concept of field of values, denoted by <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>⋅</mi><mo>)</mo></mrow></mrow></math></span>, is used to prove a sufficient condition for unconditional stability of these methods: if <span><math><mi>A</mi></math></span> is Hermitian, IMEX-BDF2 is unconditionally stable whenever <span><math><mrow><mi>F</mi><mrow><mo>(</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>B</mi><mo>)</mo></mrow></mrow></math></span> is contained in the disk centered at 0 and radius <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></math></span>, <span><math><mrow><mi>D</mi><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mo>)</mo></mrow></mrow></math></span>, while IMEX-BDF3 is unconditionally stable whenever <span><math><mrow><mi>F</mi><mrow><mo>(</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>B</mi><mo>)</mo></mrow><mo>⊆</mo><mi>D</mi><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>7</mn></mrow></mfrac><mo>)</mo></mrow></mrow></math></span>. Furthermore, sufficient conditions are derived to ensure stability, but according to the step size as a function of the radius of the disk containing <span><math><mrow><mi>F</mi><mrow><mo>(</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>B</mi><mo>)</mo></mrow></mrow></math></span>. The approach developed herein is illustrated through several examples in which the discussed theory is applied not only to DDEs, but also to parabolic problems given by partial delay differential equations (PDDEs) with a diffusion term.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117044"},"PeriodicalIF":2.6,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Representing with probabilistic ordered Bell and degenerate ordered Bell polynomials","authors":"Dae San Kim ,&nbsp;Taekyun Kim","doi":"10.1016/j.cam.2025.117122","DOIUrl":"10.1016/j.cam.2025.117122","url":null,"abstract":"<div><div>This paper explores the representation of arbitrary polynomials in terms of probabilistic ordered Bell polynomials and probabilistic degenerate ordered Bell polynomials associated with a random variable <span><math><mi>Y</mi></math></span>, whose moment generating function exists in a neighborhood of the origin. We extend this investigation to their higher-order counterparts. Employing umbral calculus, we derive explicit formulas and illustrate our findings with relevant examples.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117122"},"PeriodicalIF":2.6,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A remark on a special class of Volterra–Fredholm integral equations","authors":"Giuseppe Mastroianni ,&nbsp;Incoronata Notarangelo","doi":"10.1016/j.cam.2025.117119","DOIUrl":"10.1016/j.cam.2025.117119","url":null,"abstract":"<div><div>We propose a global method based on Lagrange interpolation at Jacobi nodes to approximate the solution of second-kind Volterra–Fredholm integral equations on the interval <span><math><mrow><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span>. The considered equations involve kernels with a multiple zero at the origin and Jacobi-type weight functions, allowing for algebraic endpoint singularities in the data. Accordingly, the problem is studied in suitable weighted spaces of continuous functions.</div><div>We prove the stability and convergence of our numerical method and derive explicit a priori error estimates in the weighted uniform norm, showing that the approximation essentially achieves the convergence rate of the best weighted polynomial approximation, up to an additional logarithmic factor <span><math><mrow><mo>log</mo><mi>m</mi></mrow></math></span>. Some numerical experiments are presented to illustrate the accuracy and efficiency of the proposed approach.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117119"},"PeriodicalIF":2.6,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Application of fractional-order hybrid Chelyshkov functions for solving a general class of fractional integro-differential equations with weakly singular kernels","authors":"Amir Hossein Taleshian ,&nbsp;Somayeh Nemati ,&nbsp;Pedro M. Lima","doi":"10.1016/j.cam.2025.117110","DOIUrl":"10.1016/j.cam.2025.117110","url":null,"abstract":"<div><div>In recent years, various fractional-order basis functions have been developed to tackle different types of fractional problems. This paper introduces a new class of fractional-order hybrid functions constructed from block-pulse functions and Chelyshkov polynomials. By applying the Riemann–Liouville integral operator, we derive explicit results using the closed form of Chelyshkov polynomials. These results are then employed to develop a numerical scheme for solving a general class of fractional integro-differential equations with weakly singular kernels. The approach, combined with the essential properties of the Caputo derivative and the Riemann–Liouville operator, leads to the definition of remainders associated with the main problem. By selecting suitable collocation points, the problem is transformed into a solvable system of equations. An error bound is established for the proposed approximation, and the effectiveness of the method is demonstrated through several illustrative examples.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117110"},"PeriodicalIF":2.6,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Conditions for preserving transform order relations of identically distributed component lifetimes by system lifetimes","authors":"Tomasz Rychlik ,&nbsp;Magdalena Szymkowiak","doi":"10.1016/j.cam.2025.117109","DOIUrl":"10.1016/j.cam.2025.117109","url":null,"abstract":"<div><div>We describe conditions for preserving relations with given distributions in the transform orders: convex transform, star, and superadditive ones of the marginal distributions of identically distributed component lifetimes by semicoherent system lifetimes. If the distinguished extremal element of the family has a left bounded support, then the conditions are necessary and sufficient. In particular, we specify the conditions for preserving the monotone generalized failure rates and their reversed versions, generalized monotone failure rates on the average, generalized new better and worse than used, and decreasing log-odds rate properties. The conditions depend on the minimal cut sets of the system and the copula of dependence among the component lifetimes. An alternative conditions are based on the respective minimal path sets and survival copula.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117109"},"PeriodicalIF":2.6,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Approximate solution to solve nonlinear Volterra integral equations with discontinuous kernels using shifted alternative Legendre polynomials","authors":"Fatemeh Mohammadi,&nbsp;Farshid Mirzaee,&nbsp;Erfan Solhi","doi":"10.1016/j.cam.2025.117111","DOIUrl":"10.1016/j.cam.2025.117111","url":null,"abstract":"<div><div>We consider nonlinear Volterra integral equations of the second kind with discontinuous kernels, which present significant analytical and numerical challenges due to the combined presence of nonlinearity and kernel discontinuity. To address these difficulties, we develop a new method based on shifted alternative Legendre polynomials and associated operational matrices. The proposed approach approximates the unknown solution via truncated polynomial expansions and systematically transforms the original integral equation into a system of nonlinear algebraic equations through matrix-based discretization. We establish several theoretical results concerning the convergence, stability, and error bounds of the method. Numerical experiments are conducted to validate the proposed approach, demonstrating its accuracy, efficiency, and capability in handling these equations .</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117111"},"PeriodicalIF":2.6,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Kernel families of fractional derivatives","authors":"Octavian Postavaru ,&nbsp;Simona Mihaela Bibic ,&nbsp;Antonela Toma","doi":"10.1016/j.cam.2025.117097","DOIUrl":"10.1016/j.cam.2025.117097","url":null,"abstract":"<div><div>Fibonacci is known in particular due to the notion of the golden ratio, which has found great success in modeling natural phenomena. Also, based on this ratio, the Fibonacci polynomials emerged, which are employed in this work to establish an innovative family of fractional kernels. After showing that the family of kernels is well defined, we define two fractional derivatives, one of Caputo type and one of Riemann–Liouville type. Next, we demonstrate certain bound characteristics that the newly defined derivatives have. We also define the associated fractional integral for one of the family members of the newly defined derivative. Using the method of Laplace transform, we found explicit solutions for <span><math><mrow><mi>R</mi><mi>C</mi></mrow></math></span> electrical circuits, using the fractional derivative introduced in this work.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117097"},"PeriodicalIF":2.6,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"General inertial proximal stochastic mirror descent algorithm beyond Lipschitz smoothness assumption","authors":"Shuang Wang ,&nbsp;Xiaomei Dong ,&nbsp;Xue Gao","doi":"10.1016/j.cam.2025.117108","DOIUrl":"10.1016/j.cam.2025.117108","url":null,"abstract":"<div><div>In this paper, minimizing the sum of an average of finite proper closed nonconvex functions and a proper lower semicontinuous convex function over a closed convex set, is considered. We propose the general inertial proximal stochastic mirror descent (IPSMD for short) algorithm framework, which not only introduces the more general inertial technique and the variance reduced gradient estimator, but also circumvents the restrictive condition of Lipschitz smoothness by using Legendre function. In theory, we establish that the sequence generated by IPSMD algorithm globally converges to the critical point, under the condition that the objective function is semialgebraic. Besides the theoretical improvement in the convergence analysis, there are also possible computational advantages which provide an interesting option for practical problems.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117108"},"PeriodicalIF":2.6,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fractional-order supply chain finance system with conformable derivative: Chaotic dynamics, complexity analysis, and RGB color image encryption","authors":"Haneche Nabil ,&nbsp;Hamaizia Tayeb","doi":"10.1016/j.cam.2025.117105","DOIUrl":"10.1016/j.cam.2025.117105","url":null,"abstract":"<div><div>Based on the supply chain management rules, a new 4D conformable fractional-order supply chain finance system is discussed. The numerical solution of the proposed system is obtained by adopting the conformable Adomian decomposition method (CADM). Some basic dynamical characteristics are employed either numerically or analytically to demonstrate the chaotic dynamical behaviors of the new system, including equilibrium points and their stability, Lyapunov exponents spectrum, fractal dimension, bifurcation diagrams, and complexity analysis. The fractional calculus theory and computer simulations reveal that the system’s lowest order to yield chaos is 0.461. Bifurcation diagrams, phase plots, and a multiscale spectral entropy (MSE) complexity analysis validate the results. Additionally, chaos synchronization of the novel conformable fractional-order chaotic system is achieved by designing a suitable nonlinear controller, based on the stability theory of fractional-order dynamical systems. Furthermore, this paper constructs a new scheme for encrypting color images based on chaos synchronization to enhance practicality. Experiments and computer simulations are conducted to verify the performance and security of the proposed image cryptosystem.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117105"},"PeriodicalIF":2.6,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}