Journal of Computational and Applied Mathematics最新文献

{"title":"An efficient finite element solver for a nonlocal size modified Poisson–Boltzmann model of proteins in multi-species ionic solutions","authors":"Dexuan Xie ,&nbsp;Liam Jemison ,&nbsp;Yi Jiang","doi":"10.1016/j.cam.2025.117026","DOIUrl":"10.1016/j.cam.2025.117026","url":null,"abstract":"<div><div>This paper introduces a nonlocal size-modified Poisson–Boltzmann (NSMPB) model and an efficient finite element iterative solver for proteins with three-dimensional molecular structures in ionic solutions containing multiple ion species. This model is the first Poisson–Boltzmann variant to simultaneously account for both nonlocal dielectric correlations and ionic size effects. The solver is constructed from a novel solution decomposition to overcome the numerical difficulties caused by the strong singularity, nonlinearity, and nonlocality of the model. It features an efficient modified Newton iterative method, an effective damping parameter selection scheme, and two good initial iteration strategies. To facilitate and streamline protein simulations, the solver is implemented as a software package that integrates a mesh generation tool, a protein data bank file retrieval program, and the PDB2PQR package. Numerical experiments involving an ionic solution with four species, three proteins with up to 11,439 atoms, and irregular interface-fitted tetrahedral meshes with up to 1,188,840 vertices demonstrate the fast convergence of the modified Newton iterative method, the efficiency of the solver, and the high performance of the package. This package provides a valuable tool for protein simulations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117026"},"PeriodicalIF":2.6,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144902689","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":"Strongly convergent forward-reflected-anchored-backward splitting algorithms to solve iteratively variational inequalities in Hilbert spaces","authors":"Chinedu Izuchukwu ,&nbsp;Yekini Shehu","doi":"10.1016/j.cam.2025.117035","DOIUrl":"10.1016/j.cam.2025.117035","url":null,"abstract":"<div><div>In this paper, we propose two fast strongly convergent forward-reflected-anchored-backward algorithms with self-adaptive step sizes to solve variational inequalities in the framework of quasi-monotonicity and Hilbert spaces. At each iteration, the proposed algorithms require one projection onto the feasible set and one functional evaluation, a distinctive trait that gives a special attraction to our algorithms and makes our algorithms state-of-the-art algorithms among strongly convergent algorithms for variational inequalities in Hilbert spaces. The available strongly convergent algorithms in the literature on variational inequalities require more than one projection onto the feasible set and (or) more than one functional evaluation per iteration with on-line rule imposed on such algorithms when inertial versions are studied. Our proposed algorithms are computationally cheaper than other relevant strongly convergent algorithms in the literature, as evident in our numerical tests.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117035"},"PeriodicalIF":2.6,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144921403","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":"Multinode Shepard functions and tensor product polynomial interpolation: Applications to Digital Elevation Models","authors":"Domingo Barrera ,&nbsp;Francesco Dell’Accio ,&nbsp;Filomena Di Tommaso ,&nbsp;Salah Eddargani ,&nbsp;María José Ibáñez ,&nbsp;Francesco Larosa ,&nbsp;Federico Nudo ,&nbsp;Juan F. Reinoso","doi":"10.1016/j.cam.2025.117036","DOIUrl":"10.1016/j.cam.2025.117036","url":null,"abstract":"<div><div>The paper presents an in-depth exploration of the multinode Shepard interpolant on a regular rectangular grid, demonstrating its efficacy in reconstructing surfaces from DEM data. Additionally, we study the approximation order associated to this interpolant and present a detailed algorithm for reconstructing surfaces. Numerical tests showcase the effectiveness of the proposed algorithm.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117036"},"PeriodicalIF":2.6,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144890716","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":"An extended virtual element method for nearly incompressible linear elasticity interface problems","authors":"Hong Zhang ,&nbsp;Jinru Chen ,&nbsp;Feng Wang ,&nbsp;Xianyan Zheng","doi":"10.1016/j.cam.2025.116989","DOIUrl":"10.1016/j.cam.2025.116989","url":null,"abstract":"<div><div>In this paper, we propose an extended virtual element method for solving nearly incompressible linear elasticity interface problems in mixed form on interface-unfitted polygonal meshes. An approximation form is presented by adding some stabilization terms and special terms along the edges of interface elements. We derive an inf–sup stability and the optimal error estimates, which are uniform with respect to mesh size, Lam<span><math><mover><mrow><mi>e</mi></mrow><mrow><mo>́</mo></mrow></mover></math></span> constants and how the interface intersects the polygonal meshes. Several numerical experiments are given to confirm our theoretical results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 116989"},"PeriodicalIF":2.6,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892273","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":"Pricing of vulnerable option under affine stochastic volatility with simultaneous jumps model","authors":"Guodong Wang","doi":"10.1016/j.cam.2025.117033","DOIUrl":"10.1016/j.cam.2025.117033","url":null,"abstract":"<div><div>This article investigates the pricing problem of vulnerable options. We consider the default risk of these options, and assume that the dynamic evolution of the underlying asset price and its instantaneous variance can be described by an affine model that incorporates stochastic volatility with simultaneous jumps. The default intensity and risk-free interest rate are assumed to be random and satisfy the CIR model. An analytical formula for the option price is derived using Fourier transform techniques. Based on this pricing formula, some models for the price of the underlying asset of option and for the default intensity of the option seller are calibrated and the model parameters are estimated. The implied volatilities corresponding to the theoretical prices of the option derived from the models are calculated and compared with the implied volatilities calculated from the option market prices.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117033"},"PeriodicalIF":2.6,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144903389","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":"Numerical study of the RBF-FD parallel-in-time contour integration method for convection–diffusion equations","authors":"Andriy Sokolov ,&nbsp;Pavel Barkhayev ,&nbsp;Stefan Turek","doi":"10.1016/j.cam.2025.117017","DOIUrl":"10.1016/j.cam.2025.117017","url":null,"abstract":"<div><div>In this work, we study the numerical performance of the parallel-in-time contour integral method for one-dimensional differential equations of convection–diffusion type. The considered method is based on the representation of a Dunford-Cauchy integral along a contour which encompasses the spectrum of an unbounded infinitesimal operator <span><math><mi>A</mi></math></span> corresponding to the equation. The discrete operator is constructed as a Radial Basis Function-generated Finite Differences (RBF-FD) discretization of diffusion and advective, resp. convective, terms. Its accuracy and performance as a part of the contour integration method is compared with those by finite difference approaches. A contour is chosen to be of elliptic shape with varying number of cubature points. Numerical performance of the contour integral method is compared with sequential-in-time realizations of the <span><math><mi>θ</mi></math></span>-scheme where discrete operators have similar discretizations by finite differences. The studied algorithm is <span><math><mrow><mn>2</mn><msub><mrow><mi>N</mi></mrow><mrow><mtext>time</mtext></mrow></msub><mspace></mspace><msub><mrow><mi>N</mi></mrow><mrow><mtext>cub</mtext></mrow></msub></mrow></math></span> parallelizable, where <span><math><msub><mrow><mi>N</mi></mrow><mrow><mtext>time</mtext></mrow></msub></math></span> is the number of time points at which the numerical solution is computed and <span><math><msub><mrow><mi>N</mi></mrow><mrow><mtext>cub</mtext></mrow></msub></math></span> is the number of cubature points on the contour. Its efficiency, however, strongly depends on the performance of the linear solver used for the resolvent part at each cubature point on the contour. In this work, we thoroughly examine the selection of a linear solver and analyze its performance with respect to various problem parameters. The proposed method is flexible in the choice of discretization techniques in space and can be readily extended to multiple dimensions.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117017"},"PeriodicalIF":2.6,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144903406","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":"Input-independent and Krawtchouk-parameter-independent parallel model order reduction based on Krawtchouk moments and block DFT for two-dimensional discrete-time systems","authors":"Zhen Li ,&nbsp;Kangli Xu","doi":"10.1016/j.cam.2025.117031","DOIUrl":"10.1016/j.cam.2025.117031","url":null,"abstract":"<div><div>This paper proposes a novel parallel model order reduction (MOR) method for two-dimensional discrete-time systems, utilizing Krawtchouk moments and block discrete Fourier transform (DFT). The proposed MOR method is independent of both inputs and Krawtchouk parameters. By exploiting the difference relations of Krawtchouk polynomials and the analytic identity theorem, we derive the explicit expressions for the Krawtchouk moments of the state, which traditionally dependent on the inputs and polynomial parameters. We then construct a projection subspace that is independent of both inputs and Krawtchouk parameters and equivalent to the subspace spanned by the Krawtchouk moments. Moreover, we propose a parallel strategy that utilizes block DFT on the block bi-diagonal <span><math><mi>ϵ</mi></math></span>-circulant matrices, enabling acceleration of the MOR process on high-performance computers. We also analyze the invertibility of the block <span><math><mi>ϵ</mi></math></span>-circulant matrices and the error of the parallel strategy. Finally, numerical experiments validate the efficiency of the proposed method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117031"},"PeriodicalIF":2.6,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886989","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":"Development of a unified framework for fractal-fractional derivatives and its application to the modified Gompertz growth equation using the Sawi transform","authors":"Arockia Deepa Uvari Antony,&nbsp;Arul Joseph Gnanaprakasam","doi":"10.1016/j.cam.2025.117028","DOIUrl":"10.1016/j.cam.2025.117028","url":null,"abstract":"<div><div>This study presents a new definition of a fractal-fractional derivative, which integrates the concepts of fractional derivatives with non-singular kernels and fractal derivatives in the sense of Caputo and Riemann. A relationship betweem the Caputo-type and Riemann-type forms of the derivative is established and its corresponding Sawi transform is rigorously derived. This formulation unifies several known fractal-fractional derivative under a single framework, including Riemann–Liouville, Caputo, Caputo–Fabrizio, Atangana–Baleanu and generalized Hattaf derivatives, all with non-singular kernels.</div><div>The Laplace transform of the proposed fractal-fractional derivative is also derived. Furthermore, the associated integral operators are studied using both the Sawi transform and Laplace transform techniques. As an application, the modified Gompertz growht model is reformulated using the Caputo–Fabrizio fractal-fractional derivative and solutions are obtained analytically using Sawi transform and Laplace transform as well as numerically.</div><div>To validate the analytical results, a numerical scheme based on a two-step Lagrange’s interpolation method is developed. An error analysis is carried out for various parameter values, using the numerical solution as the reference. A comparative analysis of the Sawi transform, Laplace transform and numerical method is conducted to assess their consistency, accuracy and efficiency in solving fractal-fractional gompertz model.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117028"},"PeriodicalIF":2.6,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144866434","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":"Unisolvence of unsymmetric random Kansa collocation by Gaussians and other analytic RBF vanishing at infinity","authors":"Alvise Sommariva,&nbsp;Marco Vianello","doi":"10.1016/j.cam.2025.116983","DOIUrl":"10.1016/j.cam.2025.116983","url":null,"abstract":"<div><div>We give a short proof of almost sure invertibility of unsymmetric random Kansa collocation matrices by a class of analytic RBF vanishing at infinity, for the Poisson equation with Dirichlet boundary conditions. Such a class includes popular Positive Definite instances such as Gaussians, Generalized Inverse MultiQuadrics and Matérn RBF. The proof works on general domains in any dimension and with any distribution of boundary collocation points, assuming that the internal collocation points are i.i.d. continuous random variables with respect to any probability density.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 116983"},"PeriodicalIF":2.6,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144912641","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":"Approximating analytic spectra of hyperbolic systems with summation-by-parts finite difference operators","authors":"Brittany A. Erickson","doi":"10.1016/j.cam.2025.117024","DOIUrl":"10.1016/j.cam.2025.117024","url":null,"abstract":"<div><div>In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to accurately discover sources of physical instabilities. By considering the perturbed equations that arise in linearized problems, we study systems in which a lower-order term can act as a source of internal energy within the system. We apply high-order accurate summation-by-parts finite difference operators, with weak enforcement of boundary conditions through the simultaneous-approximation-term technique, which leads to a provably stable numerical discretization with formal order of accuracy given by <span><math><mrow><mi>p</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></mrow></math></span> and 5. We derive analytic solutions using Laplace transform methods, which provide important ground truth to ensure numerical convergence at the correct theoretical rate. We derive the analytic spectrum and find that it is better captured with mesh refinement, although dissipative strict stability (where the growth rate of the discrete problem is bounded above by the analytic) is not obtained. We also find that sole reliance on mesh refinement can be a problematic means for determining physical growth rates as some eigenvalues emerge (and persist with mesh refinement) based on spatial order of accuracy but are non-physical. We suggest that numerical methods be used to approximate the spectra when numerical stability is guaranteed and convergence of the numerical spectra is evident with both mesh refinement and increasing order of accuracy.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117024"},"PeriodicalIF":2.6,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144866433","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}