首页 > 最新文献

Results in Applied Mathematics最新文献

英文 中文
Norm decay rates of the Fourier oscillatory integral operators for a class of homogeneous-type polynomial hybrid phases 一类同质型多项式混合相的傅立叶振荡积分算子的规范衰减率
IF 1.4 Q2 MATHEMATICS, APPLIED Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100513
Tuan Anh Pham , Nhat Huy Vu , Minh Tuan Nguyen
This paper presents a new approach to the L2(R) norm decay rates of the Fourier oscillatory integral operators for some classes of degenerate phases. In particular, the sharp norm decay rates of the Fourier oscillatory integral operators for homogeneous-type polynomial phases, and those for a class of nonsmooth polynomial hybrid phase functions are obtained.
本文提出了一种新方法,用于计算某些退化相的傅立叶振荡积分算子的 L2(R) 准则衰减率。特别是,本文得到了同质型多项式相位的傅立叶振荡积分算子的尖锐规范衰减率,以及一类非光滑多项式混合相位函数的傅立叶振荡积分算子的尖锐规范衰减率。
{"title":"Norm decay rates of the Fourier oscillatory integral operators for a class of homogeneous-type polynomial hybrid phases","authors":"Tuan Anh Pham ,&nbsp;Nhat Huy Vu ,&nbsp;Minh Tuan Nguyen","doi":"10.1016/j.rinam.2024.100513","DOIUrl":"10.1016/j.rinam.2024.100513","url":null,"abstract":"<div><div>This paper presents a new approach to the <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> norm decay rates of the Fourier oscillatory integral operators for some classes of degenerate phases. In particular, the sharp norm decay rates of the Fourier oscillatory integral operators for homogeneous-type polynomial phases, and those for a class of nonsmooth polynomial hybrid phase functions are obtained.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100513"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655286","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 capable numerical scheme for solving nonlinear Volterra delay integral equations of the third kind 解决非线性 Volterra 第三类延迟积分方程的有效数值方案
IF 1.4 Q2 MATHEMATICS, APPLIED Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100512
Rohollah Ghaedi Ghalini , Esmail Hesameddini , Hojatollah Laeli Dastjerdi
In this paper, a class of nonlinear Volterra delay integral equations of the third kind (VDIEs) is approximated by an efficient manner. At first, by using some conditions the existence and uniqueness of the solution is discussed based on the nonlinear cordial Volterra integral operators. Moreover, its convergence analysis is shown by using interpolation properties through some theorems and lemmas. Also, some examples are given and the results are compared with their exact solutions to demonstrate the reliability and capability of this algorithm.
本文以一种有效的方式逼近了一类非线性 Volterra 第三类延迟积分方程(VDIEs)。首先,基于非线性 Volterra 迟滞积分算子,利用一些条件讨论了解的存在性和唯一性。此外,通过一些定理和公理,利用插值特性对其收敛性进行了分析。此外,还给出了一些示例,并将结果与其精确解进行比较,以证明该算法的可靠性和能力。
{"title":"A capable numerical scheme for solving nonlinear Volterra delay integral equations of the third kind","authors":"Rohollah Ghaedi Ghalini ,&nbsp;Esmail Hesameddini ,&nbsp;Hojatollah Laeli Dastjerdi","doi":"10.1016/j.rinam.2024.100512","DOIUrl":"10.1016/j.rinam.2024.100512","url":null,"abstract":"<div><div>In this paper, a class of nonlinear Volterra delay integral equations of the third kind (VDIEs) is approximated by an efficient manner. At first, by using some conditions the existence and uniqueness of the solution is discussed based on the nonlinear cordial Volterra integral operators. Moreover, its convergence analysis is shown by using interpolation properties through some theorems and lemmas. Also, some examples are given and the results are compared with their exact solutions to demonstrate the reliability and capability of this algorithm.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100512"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655287","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
Existence, uniqueness, and collocation solutions using the shifted Legendre spectral method for the Hilfer fractional stochastic integro-differential equations regarding stochastic Brownian motion 关于随机布朗运动的 Hilfer 分式随机积分微分方程的存在性、唯一性和使用移位 Legendre 频谱法的配位解
IF 1.4 Q2 MATHEMATICS, APPLIED Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100504
Haneen Badawi , Omar Abu Arqub , Nabil Shawagfeh
In this paper, the existence and uniqueness of a specific class of fractional stochastic integro-differential equations considering the stochastic Brownian motion equipped with an appropriate form of a random initial condition is introduced regarding the Hilfer fractional derivative. The proofs of the existence and uniqueness of the solution are presented utilizing sensible constraints upon the deterministic and stochastic coefficients, Schauder's fixed point theorem, and some stochastic theories. Moreover, to get approximations of the exact paths solving such equations we introduce a numerical technique based upon the time-dependent spectral collocation technique considering the shifted Legendre polynomials as a basis. The underlying concept of this technique involves transforming complex equations into a set of algebraic ones by selecting an appropriate set of collocation points within the specified domain where collocation is applied. Herein, the values of the stochastic Brownian motion are calculated using the Mathematica program. For approximating the integrals, the Gauss–Legendre integration scheme is implemented. In addition, we establish the convergence concerning the presented scheme with the error estimate in detail. For this purpose, we present the graphs of maximum errors under the log-log scale. The utilized procedure is leveraged to tackle a variety of stochastic examples encompassing various types to confirm the effectiveness of the obtained theoretical and numerical results. The acquired upshots expose the efficiency and applicability of the presented methodology in the fractional stochastic field.
本文介绍了关于希尔费分式导数的一类特定分式随机积分微分方程的存在性和唯一性,该方程考虑了随机布朗运动,并配有适当形式的随机初始条件。利用对确定系数和随机系数的合理约束、Schauder 定点定理和一些随机理论,证明了解的存在性和唯一性。此外,为了获得求解此类方程的精确路径的近似值,我们引入了一种基于时变谱配位技术的数值技术,将移位 Legendre 多项式作为基础。该技术的基本概念是通过在指定域内选择一组适当的配位点,将复杂方程转换为一组代数方程,并在该域内进行配位。在这里,随机布朗运动的数值是通过 Mathematica 程序计算得出的。为了逼近积分,我们采用了高斯-列根德积分方案。此外,我们还利用误差估计详细确定了所提出方案的收敛性。为此,我们给出了对数标度下的最大误差图。我们利用所使用的程序来处理各种类型的随机例子,以证实所获得的理论和数值结果的有效性。所获得的结果揭示了所提出的方法在分数随机领域的效率和适用性。
{"title":"Existence, uniqueness, and collocation solutions using the shifted Legendre spectral method for the Hilfer fractional stochastic integro-differential equations regarding stochastic Brownian motion","authors":"Haneen Badawi ,&nbsp;Omar Abu Arqub ,&nbsp;Nabil Shawagfeh","doi":"10.1016/j.rinam.2024.100504","DOIUrl":"10.1016/j.rinam.2024.100504","url":null,"abstract":"<div><div>In this paper, the existence and uniqueness of a specific class of fractional stochastic integro-differential equations considering the stochastic Brownian motion equipped with an appropriate form of a random initial condition is introduced regarding the Hilfer fractional derivative. The proofs of the existence and uniqueness of the solution are presented utilizing sensible constraints upon the deterministic and stochastic coefficients, Schauder's fixed point theorem, and some stochastic theories. Moreover, to get approximations of the exact paths solving such equations we introduce a numerical technique based upon the time-dependent spectral collocation technique considering the shifted Legendre polynomials as a basis. The underlying concept of this technique involves transforming complex equations into a set of algebraic ones by selecting an appropriate set of collocation points within the specified domain where collocation is applied. Herein, the values of the stochastic Brownian motion are calculated using the Mathematica program. For approximating the integrals, the Gauss–Legendre integration scheme is implemented. In addition, we establish the convergence concerning the presented scheme with the error estimate in detail. For this purpose, we present the graphs of maximum errors under the log-log scale. The utilized procedure is leveraged to tackle a variety of stochastic examples encompassing various types to confirm the effectiveness of the obtained theoretical and numerical results. The acquired upshots expose the efficiency and applicability of the presented methodology in the fractional stochastic field.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100504"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579066","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
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 Q2 MATHEMATICS, APPLIED Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100509
Soufiane Moussaten
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, α-self-similar Gaussian process that does not necessarily have stationary increments, with increment exponent some β>0. We analyze the limit, in probability, of the so-called cross-variation when β in 0,2α, and we finish by providing some examples of known processes that satisfy the required assumptions.
本文研究的是二维随机过程的交叉变异,其定义是相对于一个连续的、α自相似的高斯过程(不一定有静止增量)的杨积分,增量指数为 β>0。我们分析了当β在0,2α内时,所谓交叉变异的概率极限,最后提供了一些满足所需假设的已知过程的例子。
{"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
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 Q2 MATHEMATICS, APPLIED Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100515
Abdelbaki Choucha , Salah Boulaaras , Fares Yazid , Rashid Jan , Ibrahim Mekawy
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.
具有声学和分数边界条件的非线性波方程,再加上对数源项和延迟项,因其能够模拟复杂系统、促进数学理论的发展以及广泛适用于现实问题而备受瞩目。本文研究了包含对数源项和延迟项、同时受分数边界条件和声学边界条件制约的波方程的全局存在性和一般衰减解。本文在各种假设条件下分析了解的全局存在性,并通过构建和应用合适的 Lyapunov 函数确定了一般衰减行为。
{"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 Q2 MATHEMATICS, APPLIED Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100507
Alicia Cordero , Renso V. Rojas-Hiciano , Juan R. Torregrosa , Maria P. Vassileva
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.
我们提出了用高稳定性和低成本迭代法求解一阶准线性偏微分方程(PDEs)的三种新方法。第一种是在特定条件下高效收敛的新数值版特征法。接下来的两种方法最初采用的是无条件稳定的 Crank-Nicolson 方法,该方法引出了一个非线性方程组。在其中一种方法中,我们使用首个四阶系统最优方案(埃尔马科夫超家族)来求解该系统。在另一种方法中,我们使用了一种名为 JARM 解耦的新技术,对方案进行了修改,大大降低了方案的复杂性。与传统的求解方法相比,这是一个实质性的改进。在分析一些非线性 PDEs 的解法时,我们检验了这三种方法的高数值性能。
{"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
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 Q2 MATHEMATICS, APPLIED Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100503
José Fernández Goycoolea , Luis H. Herrera , Pablo Pérez-Lantero , Carlos Seara
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 O(n2log2n) 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.
红蓝两色平面中一组点的粗细度是衡量这些点混合在一起的程度。它具有吸引人的理论特性,包括与接受良好聚类分区的点集倾向相关联。然而,精确计算它的计算成本很高。本文介绍了使用断头台分区方法计算粗度的概念,并提出了计算这种断头台粗度的高效算法:一种自顶向下的方法和一种动态编程方法,这两种方法都实现了多项式时间和空间复杂度。最后,还提出了一种更快的 O(n2log2n) 多项式时间算法,利用几何数据结构计算被称为两级断头台粗度的简化版测量。这些限制建立了一般断头台粗度的下限,从而可以开发出更高效的计算算法。
{"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 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 Q2 MATHEMATICS, APPLIED Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100510
F. Afiatdoust , M.H. Heydari , M.M. Hosseini , M. Mohseni Moghadam
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.
本研究的重点是设计一种多步骤技术,即逐块技术,为一类非线性分式二维 Volterra 积分微分方程提供数值解。所提出的技术是一种基于罗姆伯格数值积分公式的逐块方法,无需初始起始值,即可在某些节点同时获得高精度解。利用 Gronwall 不等式对上述方程的收敛分析进行了研究。通过几个数值测试,证明了该程序的准确性、速度和良好性能。
{"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 Q2 MATHEMATICS, APPLIED Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100508
Abdullo Hayotov , Samandar Babaev
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.
这项研究考虑了希尔伯特空间中用于积分方程数值逼近的最优正交公式。它讨论了用正交公式求解积分方程的顺序。在希尔伯特空间中构建了带权重的最优正交公式。利用构建的最优正交公式和梯形法则给出了求解积分方程的算法。根据这些算法求解了几个积分方程。
{"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
Induction of patterns through crowding in a cross-diffusion model 通过交叉扩散模型中的拥挤诱导模式
IF 1.4 Q2 MATHEMATICS, APPLIED Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100506
Mohammed Aldandani , John Ward , Fordyce A. Davidson
In this paper we focus on pattern formation in systems of interacting populations. We show that if one considers these populations to be “crowded” in a way that is defined below, then cross-diffusion terms appear naturally. Moreover, we show that these additional cross-diffusion terms can generate stable spatial patterns that are not manifest in the corresponding standard “dilute” formulation. This result demonstrates the need for care when choosing standard Fickian diffusion as the default in applications to population dynamics.
在本文中,我们将重点研究相互作用种群系统中的模式形成。我们发现,如果按照下文定义的方式将这些种群视为 "拥挤 "的,那么交叉扩散项就会自然出现。此外,我们还证明,这些额外的交叉扩散项可以产生稳定的空间模式,而这些模式在相应的标准 "稀释 "公式中并不明显。这一结果表明,在人口动力学应用中,选择标准费克扩散作为默认值时需要小心谨慎。
{"title":"Induction of patterns through crowding in a cross-diffusion model","authors":"Mohammed Aldandani ,&nbsp;John Ward ,&nbsp;Fordyce A. Davidson","doi":"10.1016/j.rinam.2024.100506","DOIUrl":"10.1016/j.rinam.2024.100506","url":null,"abstract":"<div><div>In this paper we focus on pattern formation in systems of interacting populations. We show that if one considers these populations to be “crowded” in a way that is defined below, then cross-diffusion terms appear naturally. Moreover, we show that these additional cross-diffusion terms can generate stable spatial patterns that are not manifest in the corresponding standard “dilute” formulation. This result demonstrates the need for care when choosing standard Fickian diffusion as the default in applications to population dynamics.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100506"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579065","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
期刊
Results in Applied Mathematics
全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1