Journal of Computational and Applied Mathematics最新文献

{"title":"Efficient high-order algorithm for nonlinear functional mixed integral equations","authors":"Chinedu Nwaigwe","doi":"10.1016/j.cam.2025.117096","DOIUrl":"10.1016/j.cam.2025.117096","url":null,"abstract":"<div><div>Despite the wide applications of nonlinear functional mixed Volterra-Fredholm equations (VFIEs), not much attention has been paid to their numerical analysis. Further, a well-known challenge in solving nonlinear integral equations is the problem of simultaneously achieving high-order accuracy, computational efficiency and avoiding to solve nonlinear algebraic systems. For contraction maps in Banach spaces, fixed-point iterative methods can address the problem of solving systems. However, the issues of computational efficiency, high-order accuracy, and approximation of functional VFIEs remain largely unaddressed. In this article, a new cubature rule is proposed and used to develop a high (fourth) order method for nonlinear functional mixed VFIEs. To ensure computational efficiency and avoid solving systems, a Gauss–Seidel-type algorithm (GSTA) is formulated. In this case of GSTA, the convergence proof becomes quite challenging (no wonder the inefficient Jacobi-type idea is very popular in the literature). We use the Banach contraction principle and mathematical induction to rigorously prove the fourth-order convergence of the method. Several numerical examples are used to verify the theoretical convergence results. It is our belief that both the numerical scheme and convergence proof presented in this paper will serve researchers in devising and analyzing efficient, high-order schemes for other integral equations, even in higher dimensions.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117096"},"PeriodicalIF":2.6,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159790","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":"Temporal error estimates of the BDF2 numerical scheme with variable time steps for the square phase-field crystal model","authors":"Danxia Wang ,&nbsp;Jiongzhuo Lv ,&nbsp;Jun Zhang ,&nbsp;Hongen Jia","doi":"10.1016/j.cam.2025.117093","DOIUrl":"10.1016/j.cam.2025.117093","url":null,"abstract":"<div><div>In this study, we propose a temporally adaptive semi-discrete computational approach for the square phase-field crystal (SPFC) model, which adopts the variable-time-step BDF2 (VBDF2) temporal discretization. By overcoming the difficulties caused by its high-order non-linear term <span><math><mrow><mi>Δ</mi><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><msup><mrow><mrow><mo>|</mo><mo>∇</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mo>∇</mo><mi>u</mi><mo>)</mo></mrow></mrow></math></span> and complex variable-time-step coefficients, we rigorously prove the unconditional energy stability and convergence results of this scheme. Moreover, we design an adaptive time-stepping algorithm to improve the computational efficiency while guaranteeing the precision. Finally, some numerical simulations validate the previous theoretical analysis.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117093"},"PeriodicalIF":2.6,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222812","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":"Parallel Computation of functions of matrices and their action on vectors for exponential integrators","authors":"Sergio Blanes","doi":"10.1016/j.cam.2025.117090","DOIUrl":"10.1016/j.cam.2025.117090","url":null,"abstract":"<div><div>We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming and can improve the performance of exponential integrators. Solving appropriate linear systems of equations in parallel (or computing the inverse of several matrices) and with a proper linear combination of the results, allows us to obtain new high order approximations to the desired functions of matrices. An error analysis to obtain forward and backward error bounds is presented. The coefficients of each method, which depends on the number of processors, can be adjusted to improve the accuracy, the stability or to reduce the round off errors of the methods. We illustrate this procedure by explicitly constructing some methods which are then tested on several numerical examples.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117090"},"PeriodicalIF":2.6,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159852","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":"Interpolation of α-harmonic functions on a circle","authors":"D. Lj. Djukić ,&nbsp;N.M. Mutavdžić ,&nbsp;R.M. Mutavdžić Djukić","doi":"10.1016/j.cam.2025.117062","DOIUrl":"10.1016/j.cam.2025.117062","url":null,"abstract":"<div><div>Similarly to harmonic functions, an <span><math><mi>α</mi></math></span>-harmonic function <span><math><mi>u</mi></math></span> on the unit disc <span><math><mi>D</mi></math></span> is uniquely determined by its values on the boundary of the disc <span><math><mrow><mi>∂</mi><mi>D</mi></mrow></math></span>. Depending on <span><math><mi>α</mi></math></span>, we investigate interpolatory formulas for approximating <span><math><mrow><mi>u</mi><mrow><mo>(</mo><mi>ζ</mi><mo>)</mo></mrow></mrow></math></span> for any given <span><math><mi>ζ</mi></math></span>, as a weighted sum of values of <span><math><mi>u</mi></math></span> at <span><math><mi>n</mi></math></span> nodes on <span><math><mrow><mi>∂</mi><mi>D</mi></mrow></math></span>. We show how to construct such formulas of highest possible algebraic degree of exactness and discuss their convergence.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117062"},"PeriodicalIF":2.6,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222810","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":"New characterizations of the diamond partial order","authors":"D.E. Ferreyra ,&nbsp;F.E. Levis ,&nbsp;G. Maharana ,&nbsp;V. Orquera","doi":"10.1016/j.cam.2025.117087","DOIUrl":"10.1016/j.cam.2025.117087","url":null,"abstract":"<div><div>Baksalary and Hauke introduced the diamond partial order in 1990, which we revisit in this paper. This order was defined on the set of rectangular matrices and is the same as the star and minus partial orders for partial isometries. New ways of describing and studying the diamond partial order are being looked into in this paper. Particularly, we present a new characterization by using an additivity property of the column spaces. Additionally, we also study the relationship between the left (resp., right) star and diamond partial orders. Specifically, we obtain conditions in which the diamond partial order means the left (resp., right) star partial order. The reverse order law for the Moore–Penrose inverse is characterized when <span><math><mi>A</mi></math></span> is below <span><math><mi>B</mi></math></span> under the diamond partial order. Finally, an interesting way of describing bi-dagger matrices is found. We also provide an algorithm to construct two rectangular matrices that are ordered under the diamond partial order. Numerical examples are given in order to confirm our results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117087"},"PeriodicalIF":2.6,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159768","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":"Magnetisation moment of a bounded 3D sample: Asymptotic recovery from planar measurements on a large disc","authors":"Dmitry Ponomarev","doi":"10.1016/j.cam.2025.117085","DOIUrl":"10.1016/j.cam.2025.117085","url":null,"abstract":"<div><div>Inverse magnetisation problem consists in inferring information about a magnetic source from measurements of its magnetic field. Unlike a general magnetisation distribution, the total magnetisation (net moment) of the source is a quantity that theoretically can be uniquely determined from the field. At the same time, it is often the most useful quantity for practical applications (on large and small scales) such as detection of a magnetic anomaly in magnetic prospection problem or finding the overall strength and mean direction of the magnetisation distribution of a magnetised rock sample. It is known that the net moment components can be explicitly estimated using the so-called Helbig’s integrals which involve integration of the magnetic field data on the plane against simple polynomials. Evaluation of these integrals requires knowledge of the magnetic field data on a large region or the use of ad hoc methods to compensate for the lack thereof. In this paper, we derive higher-order analogs of Helbig’s integrals which permit estimation of total magnetisation components in terms of measurement data available on a smaller region. Motivated by a concrete experimental setup for analysing remanent magnetisation of rock samples with a scanning microscope, we also extend Helbig’s integrals to the situation when knowledge of only one field component is necessary. Moreover, apart from derivation of these novel formulas, we rigorously prove their accuracy. The presented approach, based on an appropriate splitting in the Fourier domain and estimates of oscillatory integrals (involving both small and large parameters), elucidates the derivation of asymptotic formulas for the net moment components to an arbitrary order, a possibility that was previously unclear. The obtained results are illustrated numerically and their robustness with respect to the noise is discussed.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117085"},"PeriodicalIF":2.6,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159804","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":"Symmetric truncated Freud polynomials","authors":"Edmundo J. Huertas ,&nbsp;Alberto Lastra ,&nbsp;Francisco Marcellán ,&nbsp;Víctor Soto-Larrosa","doi":"10.1016/j.cam.2025.117080","DOIUrl":"10.1016/j.cam.2025.117080","url":null,"abstract":"<div><div>We define the family of symmetric truncated Freud polynomials <span><math><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>;</mo><mi>z</mi><mo>)</mo></mrow></mrow></math></span>, orthogonal with respect to the linear functional <span><math><mi>u</mi></math></span> defined by <span><span><span><math><mrow><mrow><mo>〈</mo><mi>u</mi><mo>,</mo><mi>p</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>〉</mo></mrow><mo>=</mo><msubsup><mrow><mo>∫</mo></mrow><mrow><mo>−</mo><mi>z</mi></mrow><mrow><mi>z</mi></mrow></msubsup><mi>p</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></msup><mi>d</mi><mi>x</mi><mo>,</mo><mspace></mspace><mi>p</mi><mo>∈</mo><mi>P</mi><mo>,</mo><mspace></mspace><mi>z</mi><mo>&gt;</mo><mn>0</mn><mo>.</mo></mrow></math></span></span></span>The semiclassical character of <span><math><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>;</mo><mi>z</mi><mo>)</mo></mrow></mrow></math></span> as polynomials of class 4 is stated. As a consequence, several properties of <span><math><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>;</mo><mi>z</mi><mo>)</mo></mrow></mrow></math></span> concerning the coefficients <span><math><mrow><msub><mrow><mi>γ</mi></mrow><mrow><mi>n</mi></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></math></span> in the three-term recurrence relation they satisfy, as well as the moments and the Stieltjes function of <span><math><mi>u</mi></math></span>, are studied. Ladder operators associated with such a linear functional and the holonomic equation satisfied by the polynomials <span><math><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>;</mo><mi>z</mi><mo>)</mo></mrow></mrow></math></span> are deduced. Additionally, an electrostatic interpretation of their zeros and their dynamics with respect to the parameter <span><math><mi>z</mi></math></span> are provided. We also consider a rescaled orthonormal sequence <span><math><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>;</mo><mi>z</mi><mo>)</mo></mrow></mrow></math></span> supported on the fixed interval <span><math><mrow><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span>, with respect to the weight <span><math><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><msup><mrow><mi>z</mi></mrow><mrow><mn>4</mn></mrow></msup><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></msup></math></span>, and establish a relative outer asymptotic relation with the Chebyshev polynomials of the second kind in the complex domain.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117080"},"PeriodicalIF":2.6,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222181","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":"Extended consistent Riccati expansion for investigating interaction between soliton and periodic wave for Drinfel’d–Sokolov–Wilson system","authors":"Juan Wang,&nbsp;Jinfu Liang","doi":"10.1016/j.cam.2025.117083","DOIUrl":"10.1016/j.cam.2025.117083","url":null,"abstract":"<div><div>The consistent Riccati expansion (CRE) method is extended and applied to derive interaction solutions of the Drinfel’d-Sokolov-Wilson (DSW) system. It has been shown that the DSW system is solvable using the extended CRE (ECRE) method. By utilizing the ECRE method, interaction solutions between solitons and Jacobi sine periodic waves are explicitly obtained for the DSW system. Furthermore, the dynamic behavior of these interactions is analyzed in detail.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117083"},"PeriodicalIF":2.6,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159801","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 NESS iteration method for singular saddle point problems","authors":"Hong Wang,&nbsp;Nai-Min Zhang","doi":"10.1016/j.cam.2025.117082","DOIUrl":"10.1016/j.cam.2025.117082","url":null,"abstract":"<div><div>Recently, Wang and Li (2019) studied a new extended shift-splitting (NESS) iteration method for solving nonsingular saddle point problems. In this paper we investigate the singular NESS (SNESS) preconditioner for solving singular saddle point problems and discuss three SNESS iterations. With the SNESS preconditioner, the splitting of the corresponding coefficient matrix is a proper splitting, which help the three SNESS iterations to converge to the generalized inverse solution. Numerical results demonstrate the effectiveness of the SNESS iterations for solving singular saddle point problems.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117082"},"PeriodicalIF":2.6,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159791","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":"High-order tensor nuclear norm with Multiway Delay-embedding Transform for color image recovery","authors":"Yu Jin,&nbsp;Ji-Cheng Li,&nbsp;Hao Shu","doi":"10.1016/j.cam.2025.117078","DOIUrl":"10.1016/j.cam.2025.117078","url":null,"abstract":"<div><div>Recently, Multiway Delay-embedding Transform (MDT)-based low-rank tensor completion has achieved a lot of attention for color image recovery. However, existing studies mostly focus on tensor decomposition to encode the low-rankness of the Hankel tensor derived from MDT, which are sensitive to the predefined rank and limit the recovery performance. Aiming at addressing this issue, in this paper, we use the High-order Tensor Nuclear Norm (HTNN) to approximate the Hankel tensor rank, thus a new model named MDT-HTNN is proposed for low-rank tensor completion. Efficient algorithm based on the alternating direction method of multipliers (ADMM) is developed to solve the proposed model and its convergence analysis is discussed in detail. Extensive experiments on a series of color images and MRI illustrate that our proposed algorithm significantly improve the recovery accuracy. Specifically, under multiple sampling rate settings for multiple color images, the average PSNR value increased by 14.8% and the CPU time decreased by 89.5% compared with the classical MDT-Tucker method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117078"},"PeriodicalIF":2.6,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159796","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}