Journal of Computational and Applied Mathematics最新文献_第8页

A fully-decoupled, second-order accurate, positivity-preserving and energy stable scheme for a two-phase flow system with ions transport

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-02-18 DOI: 10.1016/j.cam.2025.116573

Mingyang Pan , Chengxing Fu , Liu Yang , Dongdong He

{"title":"A fully-decoupled, second-order accurate, positivity-preserving and energy stable scheme for a two-phase flow system with ions transport","authors":"Mingyang Pan , Chengxing Fu , Liu Yang , Dongdong He","doi":"10.1016/j.cam.2025.116573","DOIUrl":"10.1016/j.cam.2025.116573","url":null,"abstract":"<div><div>Two-phase immiscible electrohydrodynamic flows appeared in many scientific and industrial areas are usually modelled by using the Navier–Stokes equations for fluid flow, the Cahn–Hilliard equation for dynamic interface and the Poisson–Nernst–Planck equations for ions transport. In this paper, a linear, second-order accurate, positivity-preserving and unconditionally energy stable scheme is proposed for the Navier–Stokes–Cahn–Hilliard system with ions transport. To design the scheme, a series of equivalent reformulations of the system are performed. A square root transformation is first introduced to numerically preserve the positivity of ion concentrations. Then, an auxiliary ordinary differential equation is constructed exploiting the nonlinear coupling terms, which follows the “zero-energy-contribution” principle. Finally, the scalar auxiliary variable method is adopted to linearize the nonlinear chemical potentials, and the unconditional energy stability is strictly proved. For solving the obtained scheme, we use these auxiliary variables to split the linear scheme into several sub-systems that can be solved independently at each time step. The finite element method is used for the spatial discretizations. Several numerical examples are presented to illustrate the accuracy and stability of the new scheme, and to demonstrate the impact of mobile charge carriers on the dynamics of two-phase flows and the dripping phenomena of water droplets.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"465 ","pages":"Article 116573"},"PeriodicalIF":2.1,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454311","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}

引用次数: 0

An implicit–explicit BDF2 method with variable time steps for the Ericksen–Leslie model

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-02-17 DOI: 10.1016/j.cam.2025.116574

Xin Zhang , Danxia Wang , Jianwen Zhang , Hongen Jia

引用次数: 0

Analytical solutions for the generalized (2+1)–dimensional Konopelchenko–Dubrovsky equation via Lie symmetry analysis

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-02-15 DOI: 10.1016/j.cam.2025.116564

Tapan Kumar Muduli, Purnima Satapathy

{"title":"Analytical solutions for the generalized (2+1)–dimensional Konopelchenko–Dubrovsky equation via Lie symmetry analysis","authors":"Tapan Kumar Muduli, Purnima Satapathy","doi":"10.1016/j.cam.2025.116564","DOIUrl":"10.1016/j.cam.2025.116564","url":null,"abstract":"<div><div>In this study, we examine the (2+1)–dimensional Konopelchenko–Dubrovsky (KD) equation, which models the dynamics of a two-layer fluid in shallow water near ocean shores and within a stratified atmosphere. Here, we focus on obtaining similarity solutions to the KD equation by applying Lie symmetry analysis. At first, five–dimensional Lie point symmetries are found by generalizing the invariance criterion for the integro differential equation. Further, two–dimensional optimal classification is performed for the five–dimensional Lie algebra. Moreover, invariant solutions like parabolic type and inverted bell-shaped solutions are obtained for different classes of two–dimensional optimal sets. Additionally, a special solution in terms of Airy functions is obtained for the KD equation, which is derived from the second Painlevé equation <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>I</mi><mi>I</mi></mrow></msub></math></span>. Finally, physically relevant solutions including traveling wave solutions, notably kink-type solitons, and multi solitons, are derived through traveling wave transformations, and all solutions are represented graphically.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"465 ","pages":"Article 116564"},"PeriodicalIF":2.1,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454309","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}

引用次数: 0

An improved fast approximation to two-sided variable-order space-fractional diffusion equation and its preconditioning 双面变阶空间分数扩散方程的改进型快速近似及其预处理

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-02-10 DOI: 10.1016/j.cam.2025.116555

Xiaofeng Guo , Jianyu Pan

引用次数: 0

Boundedness of zeros of Sobolev orthogonal polynomials via generalised eigenvalues

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-02-10 DOI: 10.1016/j.cam.2025.116556

C. Escribano , R. Gonzalo

引用次数: 0

C1 Hermite interpolation method for septic PHoPH curves

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-02-07 DOI: 10.1016/j.cam.2025.116548

Jingxuan Li, Hwan Pyo Moon

{"title":"C1 Hermite interpolation method for septic PHoPH curves","authors":"Jingxuan Li, Hwan Pyo Moon","doi":"10.1016/j.cam.2025.116548","DOIUrl":"10.1016/j.cam.2025.116548","url":null,"abstract":"<div><div>Pythagorean hodograph(PH) curves, which are polynomial parametric curves with the polynomial speed functions, have been formulated and analyzed both on a plane and in a space separately. If a single curve satisfies both planar PH and spatial PH condition simultaneously, it is a spatial PH curve with the planar projection. This type of curves are called as PH over PH curves, or PHoPH curves, and a <span><math><msup><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> Hermite interpolation method for quintic PHoPH curves was recently reported. This article addresses the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> Hermite interpolation problem using septic PHoPH curve. Since the hodograph of a PHoPH curve is obtained by applying two successive squaring maps to a quaternion generator polynomial, the PHoPH curve is of degree <span><math><mrow><mn>4</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></math></span> when <span><math><mi>n</mi></math></span> is the degree of the generator. So the hodograph of a septic PHoPH curve is constructed not directly from a generator but from a generator and a quadratic common factor. After fixing most parameters in the quaternion generator using the end tangent data, we can streamline the problem into a system of nonlinear equations with three unknown variables, which can be readily solved by numerical methods. The existence and the number of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> PHoPH interpolators depend on the configuration of the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> Hermite data. We provide the results of extensive Monte-Carlo simulations for the feasibility analysis of this problem. We also present a few examples of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> PHoPH splines, which converges to given reference curves with the approximation order 4.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116548"},"PeriodicalIF":2.1,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143377967","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}

引用次数: 0

Two inertial-relaxed hybridized CG projection-based algorithms for solving nonlinear monotone equations applied in image restoration

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-02-06 DOI: 10.1016/j.cam.2025.116546

Xuejie Ma , Sixing Yang , Pengjie Liu

{"title":"Two inertial-relaxed hybridized CG projection-based algorithms for solving nonlinear monotone equations applied in image restoration","authors":"Xuejie Ma , Sixing Yang , Pengjie Liu","doi":"10.1016/j.cam.2025.116546","DOIUrl":"10.1016/j.cam.2025.116546","url":null,"abstract":"<div><div>In this paper, we introduce two inertial-relaxed hybridized conjugate gradient projection-based algorithms for solving nonlinear monotone equations. Compared to traditional inertial-relaxed algorithms for solving such nonlinear equations, our algorithms utilize three-step iterative information to generate inertial iterates. The search directions of two proposed algorithms each include a flexible non-zero vector and feature their own self-adaptive hybrid structure to enhance their adaptability. Both search directions satisfy the sufficient descent and trust region properties, eliminating the need for additional conditions. In the theoretical analysis of global convergence and convergence rate results, both proposed algorithms exhibit similarities. We begin by using the first proposed algorithm to establish the global convergence without requiring the Lipschitz continuity assumption. Furthermore, under additional assumptions, we demonstrate the convergence rate of this algorithm. To evaluate their effectiveness, we conduct comparative tests against existing algorithms using nonlinear equations. Moreover, the practicality of the two proposed algorithms is shown through applications on image restoration problems.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116546"},"PeriodicalIF":2.1,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143376709","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}

引用次数: 0

Construction of quasi-localized dual bases in reproducing kernel Hilbert spaces

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-02-05 DOI: 10.1016/j.cam.2025.116545

Helmut Harbrecht , Rüdiger Kempf , Michael Multerer

{"title":"Construction of quasi-localized dual bases in reproducing kernel Hilbert spaces","authors":"Helmut Harbrecht , Rüdiger Kempf , Michael Multerer","doi":"10.1016/j.cam.2025.116545","DOIUrl":"10.1016/j.cam.2025.116545","url":null,"abstract":"<div><div>A straightforward way to represent the kernel approximant of a function, known by a finite set of samples, within a reproducing kernel Hilbert space is through the canonical dual pair. The canonical dual pair consists of the basis of kernel translates and the corresponding Lagrange basis. From a numerical perspective, one is particularly interested in dual pairs such that the dual basis is <em>quasi-local</em> meaning that it can be well approximated using only a small subset of the data sites. This implies that the inverse Gramian is approximately sparse. In this case, the kernel approximant is efficiently computable by multiplying a sparse matrix with the data vector. We present two methods for finding such quasi-localized dual bases. First, we adapt the idea of localizing the Lagrange basis, which yields an approximate canonical dual pair and extend this idea to derive a new, symmetric preconditioner for kernel matrices. Second, we use samplets to obtain multiresolution versions of dual bases. Samplets are localized discrete signed measures constructed such that their respective measure integrals of polynomials up to a certain degree vanish. Therefore, the kernel matrix and its inverse are compressible to sparse matrices in samplet coordinates for asymptotically smooth kernels. We provide benchmark experiments in two spatial dimensions to demonstrate the compression power of both approaches and apply the new preconditioner to implicit surface reconstruction in computer graphics.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"465 ","pages":"Article 116545"},"PeriodicalIF":2.1,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143436843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dynamic complexity of fifth-dimensional Henon map with Lyapunov exponent, permutation entropy, bifurcation patterns and chaos

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.cam.2025.116547

Md. Asraful Islam, Ivna Ratul Hassan, Payer Ahmed

{"title":"Dynamic complexity of fifth-dimensional Henon map with Lyapunov exponent, permutation entropy, bifurcation patterns and chaos","authors":"Md. Asraful Islam, Ivna Ratul Hassan, Payer Ahmed","doi":"10.1016/j.cam.2025.116547","DOIUrl":"10.1016/j.cam.2025.116547","url":null,"abstract":"<div><div>The research analyses how the classic Henon map's adjustments affected the system's dynamical behavior and bifurcation frameworks. Analyzing the updated Henon map's parameter space reveals intricate patterns and transitions as the system bifurcates. The dynamical evolution of the map is studied through numerical simulations, providing insights into the emergence of novel features and behaviors. Furthermore, the Lyapunov exponent of the fifth-dimensional Henon map is calculated to quantify the system's sensitivity to initial conditions. The Lyapunov exponent serves as a crucial indicator of chaos and stability, aiding in the characterization of the map's complex dynamics. The paper presents dissipative, permutation entropy, basin of attraction and a comprehensive examination of the Lyapunov exponent across parameter ranges, shedding light on the system's overall stability and chaos. A number of theorems and a study on stability are demonstrated in this article. The results highlight the profound impact of modifications on the Henon map's dynamics, offering a deeper understanding of its behavior and bifurcation scenarios. This research adds to the larger body of knowledge in the areas of unusual systems and how they act in the context of the chaos hypothesis on the behavior of the Henon map. The results show that parameter adjustments substantially shape the dynamical complexity of the Henon map. This study presents a fifth-dimensional Hénon map-based encryption and random bit generator for secure image cryptography.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"466 ","pages":"Article 116547"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551034","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}

引用次数: 0

On sparse grid interpolation for American option pricing with multiple underlying assets

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-01-31 DOI: 10.1016/j.cam.2025.116544

Jiefei Yang, Guanglian Li

{"title":"On sparse grid interpolation for American option pricing with multiple underlying assets","authors":"Jiefei Yang, Guanglian Li","doi":"10.1016/j.cam.2025.116544","DOIUrl":"10.1016/j.cam.2025.116544","url":null,"abstract":"<div><div>In this work, we develop a novel efficient quadrature and sparse grid based polynomial interpolation method to price American options with multiple underlying assets. The approach is based on first formulating the pricing of American options using dynamic programming, and then employing static sparse grids to interpolate the continuation value function at each time step. To achieve high efficiency, we first transform the domain from <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> to <span><math><msup><mrow><mrow><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mi>d</mi></mrow></msup></math></span> via a scaled tanh map, and then remove the boundary singularity of the resulting multivariate function over <span><math><msup><mrow><mrow><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mi>d</mi></mrow></msup></math></span> by a bubble function and simultaneously, to significantly reduce the number of interpolation points. We rigorously establish that with a proper choice of the bubble function, the resulting function has bounded mixed derivatives up to a certain order, which provides theoretical underpinnings for the use of sparse grids. Numerical experiments for American arithmetic and geometric basket put options with the number of underlying assets up to 16 are presented to validate the effectiveness of our approach.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116544"},"PeriodicalIF":2.1,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143289443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0