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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
Results in Applied Mathematics Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100513
Tuan Anh Pham , Nhat Huy Vu , Minh Tuan Nguyen
{"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
Results in Applied Mathematics Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100512
Rohollah Ghaedi Ghalini , Esmail Hesameddini , Hojatollah Laeli Dastjerdi
{"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
Results in Applied Mathematics Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100504
Haneen Badawi , Omar Abu Arqub , Nabil Shawagfeh
{"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
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
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
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 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
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
Results in Applied Mathematics Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100506
Mohammed Aldandani , John Ward , Fordyce A. Davidson
{"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
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