Computers & Mathematics with Applications最新文献

{"title":"Chew, Goldberger & Low equations: Eigensystem analysis and applications to one-dimensional test problems","authors":"Chetan Singh ,&nbsp;Deepak Bhoriya ,&nbsp;Anshu Yadav ,&nbsp;Harish Kumar ,&nbsp;Dinshaw S. Balsara","doi":"10.1016/j.camwa.2025.04.008","DOIUrl":"10.1016/j.camwa.2025.04.008","url":null,"abstract":"<div><div>Chew, Goldberger &amp; Low (CGL) equations describe one of the simplest plasma flow models that allow anisotropic pressure, i.e., pressure is modeled using a symmetric tensor described by two scalar pressure components, one parallel to the magnetic field, another perpendicular to the magnetic field. The system of equations is a non-conservative hyperbolic system. In this work, we analyze the eigensystem of the CGL equations. We present the eigenvalues and the complete set of right eigenvectors. We also prove the linear degeneracy of some of the characteristic fields. Using the eigensystem for CGL equations, we propose HLL and HLLI Riemann solvers for the CGL system. Furthermore, we present the AFD-WENO schemes up to the seventh order in one dimension and demonstrate the performance of the schemes on several one-dimensional test cases.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"188 ","pages":"Pages 195-220"},"PeriodicalIF":2.9,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143828415","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 novel numerical scheme for Black-Scholes PDEs modeling pricing securities","authors":"Sachin Kumar,&nbsp;Srinivasan Natesan","doi":"10.1016/j.camwa.2025.04.003","DOIUrl":"10.1016/j.camwa.2025.04.003","url":null,"abstract":"<div><div>This article introduces an efficient numerical method for solving the Black-Scholes partial differential equation (PDE) that governs European options. The methodology employs the backward Euler scheme to discretize the time derivative and incorporates the non-symmetric interior penalty Galerkin method for handling the spatial derivatives. The study aims to determine optimal order error estimates in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm and discrete energy norm. In addition, the proposed method is used to determine Greeks in option pricing. We validate the theoretical results presented in this work with numerical experiments.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"190 ","pages":"Pages 57-71"},"PeriodicalIF":2.9,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143829754","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":"Performance comparison of variable-stepsize IMEX SBDF methods on advection-diffusion-reaction models","authors":"Raed Ali Mara'Beh ,&nbsp;J.M. Mantas ,&nbsp;P. González ,&nbsp;Raymond J. Spiteri","doi":"10.1016/j.camwa.2025.04.002","DOIUrl":"10.1016/j.camwa.2025.04.002","url":null,"abstract":"<div><div>Advection-diffusion-reaction (ADR) models describe transport mechanisms in fluid or solid media. They are often formulated as partial differential equations that are spatially discretized into systems of ordinary differential equations (ODEs) in time for numerical resolution. This paper investigates the performance of variable stepsize, semi-implicit, backward differentiation formula (VSSBDF) methods of up to fourth order for solving ADR models employing two different implicit-explicit splitting approaches: a <em>physics-based</em> splitting and a splitting based on a dynamic linearization of the resulting system of ODEs, called <em>jacobian splitting</em> in this paper. We develop an adaptive time-stepping and error control algorithm for VSSBDF methods up to fourth order based on a step-doubling refinement technique using estimates of the local truncation errors. Through a systematic comparison between physics-based and Jacobian splitting across six ADR test models, we evaluate the performance based on CPU times and corresponding accuracy. Our findings demonstrate the general superiority of Jacobian splitting in several experiments.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"190 ","pages":"Pages 41-56"},"PeriodicalIF":2.9,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143829753","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":"Two efficient compact ADI methods for the two-dimensional fractional Oldroyd-B model","authors":"Xinyu Diao,&nbsp;Bo Yu","doi":"10.1016/j.camwa.2025.04.009","DOIUrl":"10.1016/j.camwa.2025.04.009","url":null,"abstract":"<div><div>The objective of this paper is to present efficient numerical algorithms to resolve the two-dimensional fractional Oldroyd-B model. Firstly, two compact alternating direction implicit (ADI) methods are constructed with convergence orders <span><math><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>τ</mi></mrow><mrow><mi>min</mi><mo>⁡</mo><mo>{</mo><mn>3</mn><mo>−</mo><mi>γ</mi><mo>,</mo><mn>2</mn><mo>−</mo><mi>β</mi><mo>,</mo><mn>1</mn><mo>+</mo><mi>γ</mi><mo>−</mo><mn>2</mn><mi>β</mi><mo>}</mo></mrow></msup><mo>+</mo><msubsup><mrow><mi>h</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>h</mi></mrow><mrow><mi>y</mi></mrow><mrow><mn>4</mn></mrow></msubsup><mo>)</mo></mrow></math></span> and <span><math><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>τ</mi></mrow><mrow><mi>min</mi><mo>⁡</mo><mo>{</mo><mn>3</mn><mo>−</mo><mi>γ</mi><mo>,</mo><mn>2</mn><mo>−</mo><mi>β</mi><mo>}</mo></mrow></msup><mo>+</mo><msubsup><mrow><mi>h</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>h</mi></mrow><mrow><mi>y</mi></mrow><mrow><mn>4</mn></mrow></msubsup><mo>)</mo></mrow></math></span>, where <em>γ</em> and <em>β</em> are orders of two Caputo fractional derivatives, <em>τ</em>, <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>y</mi></mrow></msub></math></span> are the time and space step sizes, respectively. Secondly, the convergence analyses of the proposed compact ADI methods are investigated strictly utilizing the energy estimation technique. Lastly, the two compact ADI methods are implemented to confirm the effectiveness of the convergence analysis. The convergence orders of the two compact ADI methods are separately tested in the direction of time and space, the CPU times are computed compared with the direct compact scheme to demonstrate the efficiency of the derived compact ADI methods, numerical results are also compared with the existing literature. All the numerical simulation results are listed in tabular forms which manifest the validity of the derived compact ADI methods.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"190 ","pages":"Pages 72-89"},"PeriodicalIF":2.9,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143829755","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":"Nonlinear methods for shape optimization problems in liquid crystal tactoids","authors":"J.H. Adler ,&nbsp;A.S. Andrei ,&nbsp;T.J. Atherton","doi":"10.1016/j.camwa.2025.04.004","DOIUrl":"10.1016/j.camwa.2025.04.004","url":null,"abstract":"<div><div>Anisotropic fluids, such as nematic liquid crystals, can form non-spherical equilibrium shapes known as tactoids. Predicting the shape of these structures as a function of material parameters is challenging and paradigmatic of a broader class of problems that combine shape and order. Here, we consider a discrete shape optimization approach with finite elements to find the configuration of two-dimensional and three-dimensional tactoids using the Landau–de Genne framework and a Q-tensor representation. Efficient solution of the resulting constrained energy minimization problem is achieved using a quasi-Newton and nested iteration algorithm. Numerical validation is performed with benchmark solutions and compared against experimental data and earlier work. We explore physically motivated subproblems, whereby the shape and order are separately held fixed, respectively, to explore the role of both and examine material parameter dependence of the convergence. Nested iteration significantly improves both the computational cost and convergence of numerical solutions of these highly deformable materials.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 231-248"},"PeriodicalIF":2.9,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143820228","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 splitting-based KPIK method for eddy current optimal control problems in an all-at-once approach","authors":"Min-Li Zeng ,&nbsp;Martin Stoll","doi":"10.1016/j.camwa.2025.03.038","DOIUrl":"10.1016/j.camwa.2025.03.038","url":null,"abstract":"<div><div>In this paper, we explore efficient methods for discretized linear systems that arise from eddy current optimal control problems utilizing an all-at-once approach. We propose a novel low-rank matrix equation method based on a special splitting of the coefficient matrix and the Krylov-plus-inverted-Krylov (KPIK) algorithm. First, we reformulate the resulting discretized linear system into a matrix equation format. Then, by employing the KPIK algorithm, we derive a low-rank approximation solution. This new approach is referred to as the splitting-based Krylov-plus-inverted-Krylov (SKPIK) method. The SKPIK method exhibits the potential for efficiently tackle large and sparse discretized systems, while also significantly reducing both storage requirements and computational time. Next, theoretical results regarding the existence of low-rank solutions are provided. Furthermore, numerical experiments are conducted to demonstrate the effectiveness of the proposed low-rank matrix equation method in comparison to several established classical efficient techniques.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"190 ","pages":"Pages 1-15"},"PeriodicalIF":2.9,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143791834","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 nonoverlapping domain decomposition method for extreme learning machines: Elliptic problems","authors":"Chang-Ock Lee ,&nbsp;Youngkyu Lee ,&nbsp;Byungeun Ryoo","doi":"10.1016/j.camwa.2025.04.001","DOIUrl":"10.1016/j.camwa.2025.04.001","url":null,"abstract":"<div><div>Extreme learning machine (ELM) is a methodology for solving partial differential equations (PDEs) using a single hidden layer feed-forward neural network. It presets the weight/bias coefficients in the hidden layer with random values, which remain fixed throughout the computation, and uses a linear least squares method for training the parameters of the output layer of the neural network. It is known to be much faster than Physics informed neural networks. However, classical ELM is still computationally expensive when a high level of representation is desired in the solution as this requires solving a large least squares system. In this paper, we propose a nonoverlapping domain decomposition method (DDM) for ELMs that not only reduces the training time of ELMs, but is also suitable for parallel computation. We introduce local neural networks, which are valid only at corresponding subdomains, and an auxiliary variable at the interface. We construct a system on the variable and the parameters of local neural networks. A Schur complement system on the interface can be derived by eliminating the parameters of the output layer. The auxiliary variable is then directly obtained by solving the reduced system after which the parameters for each local neural network are solved in parallel. A method for initializing the hidden layer parameters suitable for high approximation quality in large systems is also proposed. Numerical results that verify the acceleration performance of the proposed method with respect to the number of subdomains are presented.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"189 ","pages":"Pages 109-128"},"PeriodicalIF":2.9,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143791396","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":"Local Petrov-Galerkin meshfree method based on radial point interpolation for the numerical solution of 2D linear hyperbolic equations with variable coefficients","authors":"Masoud Pendar,&nbsp;Kamal Shanazari","doi":"10.1016/j.camwa.2025.03.031","DOIUrl":"10.1016/j.camwa.2025.03.031","url":null,"abstract":"<div><div>In this work, we apply the local Petrov-Galerkin method based on radial basis functions to solving the two dimensional linear hyperbolic equations with variable coefficients subject to given appropriate initial and boundary conditions. Due to the presence of variable coefficients of the differential operator, special treatment is carried out in order to apply Green's theorem and derive the variational formulation. We use the radial point interpolation method to construct shape functions and a Crank-Nicolson finite difference scheme is employed to approximate the time derivatives. The stability, convergence and error analysis of the method are also discussed and theoretically proven. Some numerical examples are presented to examine the efficiency and accuracy of the proposed method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"190 ","pages":"Pages 16-40"},"PeriodicalIF":2.9,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143791835","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":"Superconvergence analysis of the decoupled and linearized mixed finite element methods for unsteady incompressible MHD equations","authors":"Xiaochen Chu ,&nbsp;Xiangyu Shi ,&nbsp;Dongyang Shi","doi":"10.1016/j.camwa.2025.03.032","DOIUrl":"10.1016/j.camwa.2025.03.032","url":null,"abstract":"<div><div>The purpose of this article is to explore the superconvergence behavior of the first-order backward-Euler (BE) implicit/explicit fully discrete schemes for the unsteady incompressible MHD equations with low-order mixed finite element method (MFEM) by utilizing the scalar auxiliary variable (SAV) and zero-energy-contribution (ZEC) methods. Through dealing with linear terms in implicit format and nonlinear terms in explicit format, the original problem is decomposed into several subproblems, which effectively reduces the amount of calculation. Particularly, a new high-precision estimation is given, which acts as a requisite role in getting the expected results. Following this, combined with a simple, effective and economic interpolation post-processing approach, the superclose and superconvergence error estimates of the decoupled and linearized fully discrete finite element SAV-BE scheme are rigorously derived. And the derivation process is also applicable to the ZEC-BE scheme. Finally, the corresponding numerical simulations are carried out to confirm the accuracy and reliability of our theoretical findings.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"188 ","pages":"Pages 160-182"},"PeriodicalIF":2.9,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143777067","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":"Asynchronous multimodal PINN pre-train framework based on TransVNet(MPP-TV) and its application in numerical solutions of the Cauchy problem for the Hamilton-Jacobi equation","authors":"Tianhao Chen ,&nbsp;Zeyu Li ,&nbsp;Pengbo Xu ,&nbsp;Haibiao Zheng","doi":"10.1016/j.camwa.2025.03.027","DOIUrl":"10.1016/j.camwa.2025.03.027","url":null,"abstract":"<div><div>The Hamilton-Jacobi(HJ) equation represents a class of highly nonlinear partial differential equations. Classical numerical techniques, such as finite element methods, face significant challenges when addressing the numerical solutions of such nonlinear HJ equations. However, recent advances in neural network-based approaches, particularly Physics-Informed Neural Networks (PINNs) and neural operator methods, have ushered in innovative paradigms for numerically solving HJ equations. In this work, we leverage the PINN approach, infused with the concept of neural operators. By encoding and extracting features from the discretized images of functions through TransVNet, which is a novel autoencoder architecture proposed in this paper, we seamlessly integrate Hamiltonian information into PINN training, thereby establishing a novel scientific computation framework. Additionally, we incorporate the vanishing viscosity method, introducing viscosity coefficients in our model, which equips our model to tackle potential singularities in nonlinear HJ equations. These attributes signify that our MPP-TV framework paves new avenues and insights for the generalized solutions of nonlinear HJ equations.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 203-230"},"PeriodicalIF":2.9,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143777485","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}