Journal of Computational and Applied Mathematics最新文献

{"title":"Finite bivariate biorthogonal I - Konhauser polynomials","authors":"Esra Güldoğan Lekesi̇z ,&nbsp;Bayram Çeki̇m ,&nbsp;Mehmet Ali Özarslan","doi":"10.1016/j.cam.2025.117106","DOIUrl":"10.1016/j.cam.2025.117106","url":null,"abstract":"<div><div>In the present study, a finite set of biorthogonal polynomials in two variables, produced from Konhauser polynomials, is introduced. Some properties like Laplace transform, integral and operational representation, fractional calculus operators of this family are investigated. Also, we compute Fourier transform for this new set and discover a new family of finite biorthogonal functions with the help of Parseval’s identity. Further, in order to have semigroup property, we modify this finite set by adding two new parameters and construct fractional calculus operators. Thus, integral equation and integral operator are obtained for the modified version.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117106"},"PeriodicalIF":2.6,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269514","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":"Estimating landslide thickness through domain-based regularization","authors":"Lisa Borgatti ,&nbsp;Davide Donati ,&nbsp;Liwei Hu ,&nbsp;Germana Landi ,&nbsp;Fabiana Zama","doi":"10.1016/j.cam.2025.117073","DOIUrl":"10.1016/j.cam.2025.117073","url":null,"abstract":"<div><div>This paper introduces a novel domain-based regularization approach for estimating landslide thickness from surface velocity data. Such quantity is crucial for accurately assessing landslides behavior, potential impact, and associated risks. Here, we formulate the problem as an ill-posed inverse problem and propose, for its solution, a multipenalty regularization approach based on the decomposition of the landslide domain in several regions with uniform magnitude of the horizontal velocity. We extend the Balancing Principle to accommodate non-constant balancing parameters across decomposed regions. Our Domain-based Majorization-Minimization algorithm converges to solutions that satisfy this extended principle, demonstrating superior performance compared to traditional methods. Through rigorous testing on both synthetic and real-world landslide data, we show that strategic domain decomposition based on velocity field homogeneity enhances estimation accuracy. Our findings reveal that while excessive subdivision is counterproductive, identifying appropriate velocity-based macro-regions yields optimal results. This methodology provides more reliable thickness estimates crucial for landslide risk assessment and monitoring.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117073"},"PeriodicalIF":2.6,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222175","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":"Fractal cubic multiquadric quasi-interpolation","authors":"D. Kumar ,&nbsp;A.K.B. Chand ,&nbsp;P.R. Massopust","doi":"10.1016/j.cam.2025.117099","DOIUrl":"10.1016/j.cam.2025.117099","url":null,"abstract":"<div><div>In this article, we propose a novel class of fractal cubic multiquadric functions that generalize the classical cubic multiquadric functions. By employing these fractal multiquadric functions, we develop a fractal quasi-interpolation operator, denoted by <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>d</mi></mrow><mrow><mi>α</mi></mrow></msubsup></math></span>. We examine various properties of these fractal cubic multiquadric approximants, such as shape-preserving characteristics and the ability to reproduce quadratic polynomials. Error estimates for these approximants are also derived, and estimates for the box-dimension of the graphs of fractal cubic multiquadric approximants are given. Numerical examples are presented to validate these theoretical findings and highlight the benefits of the fractal quasi-interpolant <span><math><mrow><msubsup><mrow><mi>L</mi></mrow><mrow><mi>d</mi></mrow><mrow><mi>α</mi></mrow></msubsup><mi>f</mi></mrow></math></span>. Additionally, we apply the proposed fractal quasi-interpolants to solve an integral equation with a non-smooth degenerate kernel. This approach shows a high rate of convergence to the exact solution. Box-dimension results for the numerical solution of this integral equation are also established.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117099"},"PeriodicalIF":2.6,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222182","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":"Robust selection and estimation for sparse multivariate functional nonparametric additive models via regularized Huber regression","authors":"Yilun Wang ,&nbsp;Yuan Xue ,&nbsp;Yujie Li ,&nbsp;Gaorong Li","doi":"10.1016/j.cam.2025.117104","DOIUrl":"10.1016/j.cam.2025.117104","url":null,"abstract":"<div><div>In this paper, we investigate sparse functional additive models with multivariate functional predictors and a scalar response variable. This model adopts a nonparametric additive framework to flexibly incorporate multivariate functional principal component analysis (FPCA) scores, effectively capturing complex nonlinear relationships while mitigating the curse of dimensionality. To enhance robustness against outliers and heavy-tailed errors, we propose a regularized Huber regression method incorporating the component selection and smoothing operator (COSSO) penalty. The proposed approach is formulated within a reproducing kernel Hilbert space (RKHS) framework, enabling simultaneous component selection and estimation in a robust manner. Furthermore, we extend the locally adaptive majorize-minimization (LAMM) principle to develop a general iterative optimization algorithm applicable to any loss function with continuous gradients. Under mild assumptions on the error distribution (without requiring sub-Gaussian tails) and standard regularity conditions, we establish theoretical guarantees for the proposed estimator. Extensive simulation studies and a real data application to fluorescence spectroscopy demonstrate the superior performance of our method compared to existing alternatives.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117104"},"PeriodicalIF":2.6,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222183","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 second-order energy stable numerical scheme of the modified Cahn–Hilliard equation for simulating wetting phenomena","authors":"Yu Liu ,&nbsp;Yi Shi","doi":"10.1016/j.cam.2025.117103","DOIUrl":"10.1016/j.cam.2025.117103","url":null,"abstract":"<div><div>In this paper, we design a second-order unconditional energy stable numerical scheme for the modified Cahn–Hilliard phase field model simulating wetting phenomenon. We use the scalar auxiliary variable (SAV) method to transform the Cahn–Hilliard equation into an equivalent form, use second-order backward difference formula (BDF2) for time discretization and finite element method (FEM) for space discretization. A relaxation technique is employed to correct the numerical errors of the scalar auxiliary variable. The scheme is proved to be unconditionally energy stable. We perform several numerical experiments for wetting phenomena on flat, curved and rough substrates, demonstrating the capability of our proposed numerical scheme. At the same time, we also combine our numerical scheme with an adaptive time stepping strategy for acceleration.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117103"},"PeriodicalIF":2.6,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159792","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":"Valuation of American put options under a modified 4/2 stochastic volatility model","authors":"Jiling Cao ,&nbsp;Jeong-Hoon Kim ,&nbsp;Wenqiang Liu ,&nbsp;Wenjun Zhang","doi":"10.1016/j.cam.2025.117101","DOIUrl":"10.1016/j.cam.2025.117101","url":null,"abstract":"<div><div>In this paper, we study the valuation of American put options based on the 4/2 stochastic volatility model that incorporates multiscale double mean-reverting (DMR) volatility. The option price problem is transformed into a partial differential equation (PDE) problem with free boundary, which in turn leads to PDE problems for a few terms of asymptotic expansions of the option price and free boundary. The approximate American put price is decomposed into the sum of the corresponding European put price and the early exercise premium. The chosen modification of the 4/2 stochastic volatility allows for a step-by-step approach to the option price starting from the Black–Scholes price of the corresponding European option, making it easier to approximate the price of an American put option. We check the accuracy of the resultant approximate option price and free boundary by using the least squares Monte Carlo simulation method and investigate the impact of the Heston and 3/2 factors of the volatility on the option price and free boundary. We calibrate our model to real market data and benchmark it against the widely used Heston model and the 3/2 model. We also conduct a sensitivity analysis to show how small changes in model parameters influence the American put option premium and early exercise boundary, and discuss limiting scenarios when the 3/2 term vanishes or volatility becomes deterministic. In addition, two specific results are provided. We derive a semi-analytic solution for the approximate option price and free boundary when an American put option is near expiration. We also study the pricing of an American put option without an expiration date and obtain a closed-form analytic formula for the approximate option price and free boundary.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117101"},"PeriodicalIF":2.6,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222176","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":"Estimation of parameters for a system equipped with protection block","authors":"Coşkun Kuş ,&nbsp;Serkan Eryilmaz","doi":"10.1016/j.cam.2025.117102","DOIUrl":"10.1016/j.cam.2025.117102","url":null,"abstract":"<div><div>This paper studies the problem of estimating unknown parameters involved in a system which is equipped with a protection block. The system has different failure rates depending on whether the protection block is present or not, as the protection block is modeled by its own lifetime distribution and contributes an additional failure component to the system. The model is analyzed under the assumption of exponentially distributed lifetimes, leading to the study of its distributional properties and the estimation problem for its unknown parameters. Closed-form expressions for the maximum likelihood estimators are obtained. Furthermore, theoretical expectations and variances of the estimators are derived. We also discuss the stress–strength reliability estimation problem and construct confidence intervals for the associated reliability measure. Numerical results are provided to demonstrate the implementation of the proposed methods.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117102"},"PeriodicalIF":2.6,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222807","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":"Scenario tree reduction algorithms combining quantitative stability with k-medoids clustering for large-scale risk-averse multi-stage stochastics programming problems","authors":"Bingbing Ji,&nbsp;Zhiping Chen,&nbsp;Wentao Ma","doi":"10.1016/j.cam.2025.117107","DOIUrl":"10.1016/j.cam.2025.117107","url":null,"abstract":"<div><div>In this paper, we propose a novel scenario tree reduction framework derived from the quantitative stability of risk-averse multi-stage stochastic programs. We first establish the quantitative stability theorem for risk-averse multi-stage stochastic programming problems, a general scenario tree reduction model is then developed from the obtained quantitative bound, and finally we derive an error bound on the deviation between the optimal value of the multi-stage stochastic programming problem under the reduced scenario tree and that under the original scenario tree. Additionally, we introduce a new distance to measure the similarity among different nodes, and develop two scenario tree reduction algorithms utilizing the <span><math><mi>k</mi></math></span>-medoid and local search frameworks, respectively. The proposed scenario tree reduction algorithms can effectively control the error in the optimal value/decision of the optimization problem caused by the scenario tree reduction. Moreover, the low computational cost of these algorithms allows one to solve large-scale risk-averse multi-stage stochastic programs with many stages. Finally, a series of numerical experiments are carried out to demonstrate the superiority of proposed scenario tree reduction algorithms.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117107"},"PeriodicalIF":2.6,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222806","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":"Oscillatory behavior of solutions of fractional differential equations with two different derivatives","authors":"Said R. Grace ,&nbsp;G.N. Chhatria","doi":"10.1016/j.cam.2025.117098","DOIUrl":"10.1016/j.cam.2025.117098","url":null,"abstract":"<div><div>This study investigates the asymptotic and oscillatory behavior of solutions to a class of forced nonlinear fractional differential equations (FDEs) characterized by two distinct Caputo fractional derivatives of the form <span><span><span><math><mrow><msup><mrow></mrow><mrow><mi>C</mi></mrow></msup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>c</mi></mrow><mrow><mi>α</mi></mrow></msubsup><mi>Z</mi><mrow><mo>(</mo><mi>ℓ</mi><mo>)</mo></mrow><mo>+</mo><mi>a</mi><msup><mrow><mspace></mspace></mrow><mrow><mi>C</mi></mrow></msup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>c</mi></mrow><mrow><mi>β</mi></mrow></msubsup><mi>Z</mi><mrow><mo>(</mo><mi>ℓ</mi><mo>)</mo></mrow><mo>−</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>ℓ</mi><mo>,</mo><mi>Z</mi><mrow><mo>(</mo><mi>ℓ</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>=</mo><mi>e</mi><mrow><mo>(</mo><mi>ℓ</mi><mo>)</mo></mrow><mo>+</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>ℓ</mi><mo>,</mo><mi>Z</mi><mrow><mo>(</mo><mi>ℓ</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mi>c</mi><mo>&gt;</mo><mn>1</mn><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>β</mi><mo>&lt;</mo><mn>1</mn><mo>&lt;</mo><mn>1</mn><mo>+</mo><mi>β</mi><mo>≤</mo><mi>α</mi><mo>&lt;</mo><mn>2</mn></mrow></math></span>. While multi-term FDEs are known to effectively model complex multi-scale phenomena like viscoelasticity, the qualitative theory for equations where the derivatives span both the sub-diffusive (<span><math><mrow><mi>β</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span>) and super-diffusive (<span><math><mrow><mi>α</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span>) regimes remains underdeveloped. This study aims to bridge this gap. Under specific growth conditions on the nonlinear functions <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, novel sufficient criteria are established to ensure that all solutions of the equation are oscillatory. The proof technique employs a unified framework integrating the semi-group properties of integer-order calculus with fractional operators and proceeds via a counterfactual argument by assuming the existence of a non-oscillatory solution and deriving a contradiction. The results presented here significantly extend the existing oscillation theory for fractional differential equations with multiple derivatives. The theoretical findings are further illustrated with some examples.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117098"},"PeriodicalIF":2.6,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159849","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 conforming virtual element framework for the time-fractional semi-linear reaction–diffusion equation on polygonal meshes","authors":"Zaffar Mehdi Dar ,&nbsp;M. Arrutselvi ,&nbsp;Chandru Muthusamy ,&nbsp;Sundararajan Natarajan ,&nbsp;G. Manzini","doi":"10.1016/j.cam.2025.117100","DOIUrl":"10.1016/j.cam.2025.117100","url":null,"abstract":"<div><div>This article presents the virtual element method for solving a two-dimensional time-fractional semi-linear reaction–diffusion equation with a fractional derivative of order <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> in time. The methodology is based on three fundamental technical components: a fractional version of the Grünwald–Letnikov approximation, a discrete maximal regularity property, and the regularity theory associated with non-linearity. We prove the well-posedness of the discretized scheme developed for the solution of the time-fractional reaction–diffusion equation with a Lipschitz-continuous nonlinear term. The fully discrete scheme inherently maintains stability and consistency by leveraging the discrete maximal regularity and the elliptic projection operator. The convergence in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> semi-norm is validated by numerical results over regular Voronoi, distorted hexagons, and non-convex polygon mesh configurations, underlining the practical effectiveness of the proposed scheme. The numerical examples illustrated are important real time applications of the time-fractional nonlinear partial differential equations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117100"},"PeriodicalIF":2.6,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222178","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}