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Results in Applied Mathematics最新文献

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On the cross-variation of a class of stochastic processes 论一类随机过程的交叉变异
IF 1.4
Results in Applied Mathematics Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100509
Soufiane Moussaten
{"title":"On the cross-variation of a class of stochastic processes","authors":"Soufiane Moussaten","doi":"10.1016/j.rinam.2024.100509","DOIUrl":"10.1016/j.rinam.2024.100509","url":null,"abstract":"<div><div>The present paper deals with the study of the cross-variation of two-dimensional stochastic process defined using the Young integral with respect to a continuous, <span><math><mi>α</mi></math></span>-self-similar Gaussian process that does not necessarily have stationary increments, with increment exponent some <span><math><mrow><mi>β</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. We analyze the limit, in probability, of the so-called cross-variation when <span><math><mi>β</mi></math></span> in <span><math><mfenced><mrow><mn>0</mn><mo>,</mo><mn>2</mn><mi>α</mi></mrow></mfenced></math></span>, and we finish by providing some examples of known processes that satisfy the required assumptions.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100509"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Numerical solution of first kind Fredholm integral equations with semi-smooth kernel: A two-stage iterative approach
IF 1.4
Results in Applied Mathematics Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100520
Mohana Sundaram Muthuvalu , Nor Aida Zuraimi Md Noar , Harry Setiawan , Isman Kurniawan , Shaher Momani
{"title":"Numerical solution of first kind Fredholm integral equations with semi-smooth kernel: A two-stage iterative approach","authors":"Mohana Sundaram Muthuvalu ,&nbsp;Nor Aida Zuraimi Md Noar ,&nbsp;Harry Setiawan ,&nbsp;Isman Kurniawan ,&nbsp;Shaher Momani","doi":"10.1016/j.rinam.2024.100520","DOIUrl":"10.1016/j.rinam.2024.100520","url":null,"abstract":"<div><div>This paper examines two-stage iterative methods, specifically the Geometric Mean (GM) method and its variants, for solving dense linear systems associated with first-kind Fredholm integral equations with semi-smooth kernels. These equations, characterised by ill-posedness and sensitivity to input perturbations, are discretised using a composite closed Newton-Cotes quadrature scheme. The study evaluates the computational performance and accuracy of the standard GM method, also referred to as the Full-Sweep Geometric Mean (FSGM), in comparison with the Half-Sweep Geometric Mean (HSGM) and Quarter-Sweep Geometric Mean (QSGM) methods. Numerical experiments demonstrate significant reductions in computational complexity and execution time while maintaining high solution accuracy. The QSGM method achieves the best performance among the tested methods, highlighting its effectiveness in addressing computational challenges associated with first-kind Fredholm integral equations.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100520"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143141458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analyzing inverse backward problem in nonlinear integro-differential equation with memory kernel 分析带有记忆核的非线性积分微分方程中的逆向问题
IF 1.4
Results in Applied Mathematics Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100517
M.J. Huntul
{"title":"Analyzing inverse backward problem in nonlinear integro-differential equation with memory kernel","authors":"M.J. Huntul","doi":"10.1016/j.rinam.2024.100517","DOIUrl":"10.1016/j.rinam.2024.100517","url":null,"abstract":"<div><div>This paper focuses on the backward problem related to an integro-differential equation with a general convolutional derivative in time and nonlinear source terms. The existence, uniqueness, and regularity of the mild solution to the proposed problem are established under certain assumptions in a suitable space. The proposed problem is ill-posed in the sense of Hadamard. Moreover, the Fourier truncation method is used to construct a regularized solution. Finally, the convergence rate between the regularized solution and the exact solution is determined.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100517"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Results on a nonlinear wave equation with acoustic and fractional boundary conditions coupling by logarithmic source and delay terms: Global existence and asymptotic behavior of solutions 具有声学和分数边界条件的非线性波方程与对数源项和延迟项耦合的结果：解的全局存在性和渐近行为
IF 1.4
Results in Applied Mathematics Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100515
Abdelbaki Choucha , Salah Boulaaras , Fares Yazid , Rashid Jan , Ibrahim Mekawy
{"title":"Results on a nonlinear wave equation with acoustic and fractional boundary conditions coupling by logarithmic source and delay terms: Global existence and asymptotic behavior of solutions","authors":"Abdelbaki Choucha ,&nbsp;Salah Boulaaras ,&nbsp;Fares Yazid ,&nbsp;Rashid Jan ,&nbsp;Ibrahim Mekawy","doi":"10.1016/j.rinam.2024.100515","DOIUrl":"10.1016/j.rinam.2024.100515","url":null,"abstract":"<div><div>The nonlinear wave equation with acoustic and fractional boundary conditions, coupled with logarithmic source and delay terms, is notable for its capacity to model complex systems, contribute to the advancement of mathematical theory, and exhibit wide-ranging applicability to real-world problems. This paper investigates the global existence and general decay of solutions to a wave equation characterized by the inclusion of logarithmic source and delay terms, governed by both fractional and acoustic boundary conditions. The global existence of solutions is analyzed under various hypotheses, and the general decay behavior is established through the construction and application of a suitable Lyapunov function.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100515"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
High-efficiency implicit scheme for solving first-order partial differential equations 求解一阶偏微分方程的高效隐式方案
IF 1.4
Results in Applied Mathematics Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100507
Alicia Cordero , Renso V. Rojas-Hiciano , Juan R. Torregrosa , Maria P. Vassileva
{"title":"High-efficiency implicit scheme for solving first-order partial differential equations","authors":"Alicia Cordero ,&nbsp;Renso V. Rojas-Hiciano ,&nbsp;Juan R. Torregrosa ,&nbsp;Maria P. Vassileva","doi":"10.1016/j.rinam.2024.100507","DOIUrl":"10.1016/j.rinam.2024.100507","url":null,"abstract":"<div><div>We present three new approaches for solving first-order quasi-linear partial differential equations (PDEs) with iterative methods of high stability and low cost. The first is a new numerical version of the method of characteristics that converges efficiently, under certain conditions. The next two approaches initially apply the unconditionally stable Crank–Nicolson method, which induces a system of nonlinear equations. In one of them, we solve this system by using the first optimal schemes for systems of order four (Ermakov’s Hyperfamily). In the other approach, using a new technique called JARM decoupling, we perform a modification that significantly reduces the complexity of the scheme, which we solve with scalar versions of the aforementioned iterative methods. This is a substantial improvement over the conventional way of solving the system. The high numerical performance of the three approaches is checked when analyzing the resolution of some examples of nonlinear PDEs.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100507"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New discussion on trajectory controllability of time-variant impulsive neutral stochastic functional integrodifferential equations via noncompact semigroup 基于非紧半群的时变脉冲中立型随机泛函积分微分方程轨迹可控性的新讨论
IF 1.4
Results in Applied Mathematics Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100518
Dhanalakshmi Kasinathan , Ravikumar Kasinathan , Ramkumar Kasinathan , Dimplekumar Chalishajar
{"title":"New discussion on trajectory controllability of time-variant impulsive neutral stochastic functional integrodifferential equations via noncompact semigroup","authors":"Dhanalakshmi Kasinathan ,&nbsp;Ravikumar Kasinathan ,&nbsp;Ramkumar Kasinathan ,&nbsp;Dimplekumar Chalishajar","doi":"10.1016/j.rinam.2024.100518","DOIUrl":"10.1016/j.rinam.2024.100518","url":null,"abstract":"<div><div>The purpose of this paper is to determine a new discussion on trajectory-(T) controllability of time variant impulsive neutral stochastic functional integrodifferential equations (INSFIDEs) driven by fractional Brownian motion (fBm) via noncompact semigroup in a Hilbert space. Initially, with the help of the Hausdorff measure of noncompactness (HMN), the Mönch fixed point theorem and some inequality techniques, some new standards to guarantee the mild solution for INSFIDEs are obtained. The system’s T-controllability is then examined using Gronwall’s inequality. An example is given to validate the results at the end. This work is applicable to the heart disease biological system using parametric smoothing technique with modifying time variable. Our work extends the work of Boufoussi and Hajji (2012), Chen (2010), Caraballoa et al., (2011), Boudaoui et al., (2015).</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100518"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142759536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Computing the coarseness measure of a bicolored point set over guillotine partitions 计算断头台分区上双色点集的粗略度量
IF 1.4
Results in Applied Mathematics Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100503
José Fernández Goycoolea , Luis H. Herrera , Pablo Pérez-Lantero , Carlos Seara
{"title":"Computing the coarseness measure of a bicolored point set over guillotine partitions","authors":"José Fernández Goycoolea ,&nbsp;Luis H. Herrera ,&nbsp;Pablo Pérez-Lantero ,&nbsp;Carlos Seara","doi":"10.1016/j.rinam.2024.100503","DOIUrl":"10.1016/j.rinam.2024.100503","url":null,"abstract":"<div><div>The coarseness of a set of points in the plane colored red and blue is a measure of how well the points are mixed together. It has appealing theoretical properties, including a connection to the set of points tendency to accept a good clustering partition. Yet, it is computationally expensive to compute exactly. In this paper, the notion of computing the coarseness using a guillotine partition approach is introduced, and efficient algorithms for computing this guillotine coarseness are presented: a top-down approach and a dynamic programming approach, both of them achieving polynomial time and space complexities. Finally, an even faster <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mo>log</mo></mrow><mrow><mn>2</mn></mrow></msup><mi>n</mi><mo>)</mo></mrow></mrow></math></span> polynomial-time algorithm to compute a reduced version of the measurement named two-level guillotine coarseness is presented using geometric data structures for faster computations. These restrictions establish lower bounds for the general guillotine coarseness that allow the development of more efficient algorithms for computing it.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100503"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A fitted mesh robust numerical method and analysis for the singularly perturbed parabolic PDEs with a degenerate coefficient
IF 1.4
Results in Applied Mathematics Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100519
Hassan J. Al Salman , Fasika Wondimu Gelu , Ahmed A. Al Ghafli
{"title":"A fitted mesh robust numerical method and analysis for the singularly perturbed parabolic PDEs with a degenerate coefficient","authors":"Hassan J. Al Salman ,&nbsp;Fasika Wondimu Gelu ,&nbsp;Ahmed A. Al Ghafli","doi":"10.1016/j.rinam.2024.100519","DOIUrl":"10.1016/j.rinam.2024.100519","url":null,"abstract":"<div><div>In this study, we present a nearly second-order central finite difference approach for solving a singularly perturbed parabolic problem with a degenerate coefficient. The approach uses a Crank–Nicolson method to discretize the time direction on the uniform mesh and a second-order central finite difference method on the Shishkin mesh in the space direction. The solution to the problem shows a parabolic boundary layer around <span><math><mrow><mi>x</mi><mo>=</mo><mn>0</mn></mrow></math></span>. Our error estimates indicate that the suggested approach is nearly second-order <span><math><mi>ɛ</mi></math></span>-uniformly convergent both in space and time directions. Some numerical results have been generated to validate the theoretical findings. Extensive comparisons have been carried out, demonstrating that the current approach is more accurate than previous methods in the literature.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100519"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143141457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A numerical technique for a class of nonlinear fractional 2D Volterra integro-differential equations 一类非线性分式二维 Volterra 积分微分方程的数值技术
IF 1.4
Results in Applied Mathematics Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100510
F. Afiatdoust , M.H. Heydari , M.M. Hosseini , M. Mohseni Moghadam
{"title":"A numerical technique for a class of nonlinear fractional 2D Volterra integro-differential equations","authors":"F. Afiatdoust ,&nbsp;M.H. Heydari ,&nbsp;M.M. Hosseini ,&nbsp;M. Mohseni Moghadam","doi":"10.1016/j.rinam.2024.100510","DOIUrl":"10.1016/j.rinam.2024.100510","url":null,"abstract":"<div><div>The present study focuses on designing a multi-step technique, known as the block-by-block technique, to provide the numerical solution for a category of nonlinear fractional two-dimensional Volterra integro-differential equations. The proposed technique is a block-by-block method based on Romberg’s numerical integration formula, which simultaneously obtains highly accurate solutions at certain nodes without requiring initial starting values. The convergence analysis of the established method for the aforementioned equations is investigated using Gronwall’s inequality. Several numerical tests are presented to demonstrate the accuracy, speed, and good performance of the procedure.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100510"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The numerical solution of a Fredholm integral equations of the second kind by the weighted optimal quadrature formula 用加权最优正交公式数值求解弗里德霍尔姆第二类积分方程
IF 1.4
Results in Applied Mathematics Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100508
Abdullo Hayotov , Samandar Babaev
{"title":"The numerical solution of a Fredholm integral equations of the second kind by the weighted optimal quadrature formula","authors":"Abdullo Hayotov ,&nbsp;Samandar Babaev","doi":"10.1016/j.rinam.2024.100508","DOIUrl":"10.1016/j.rinam.2024.100508","url":null,"abstract":"<div><div>This work considers the optimal quadrature formula in a Hilbert space for the numerical approximation of the integral equations. It discusses the sequence of solving integral equations with quadrature formulas. An optimal quadrature formula with weight is constructed in the Hilbert space. The algorithms for solving the integral equation are given using the constructed optimal quadrature formula and trapezoidal rule. Several integral equations are solved based on these algorithms.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100508"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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