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MODIFIED COLLOCATION METHODS FOR SECOND KIND OF VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY SINGULAR HIGHLY OSCILLATORY BESSEL KERNELS 一类具有弱奇异高振荡贝塞尔核的第二类volterra积分方程的修正配位方法
4区 数学
Journal of Applied Analysis and Computation Pub Date : 2023-01-01 DOI: 10.11948/20220559
Jianyu Wang, Chunhua Fang, Guifeng Zhang, Zaiyun Zhang
{"title":"MODIFIED COLLOCATION METHODS FOR SECOND KIND OF VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY SINGULAR HIGHLY OSCILLATORY BESSEL KERNELS","authors":"Jianyu Wang, Chunhua Fang, Guifeng Zhang, Zaiyun Zhang","doi":"10.11948/20220559","DOIUrl":"https://doi.org/10.11948/20220559","url":null,"abstract":"In this paper, we investigate the second kind of Volterra integral equations with weakly sinular highly oscillatory Bessel kernels by using two collocation methods: direct high-order interpolationorder (DO) and direct Hermite interpolation (DH). Based on hypergeometric and Gamma functions, we obtain a method for solving the modified moments $ int_{0}^{1}x^{alpha}(1-x)^{beta}J_{v}(omega x)dx $. Compared with the Filon-type $ (Q_{N}^{F}) $ method, piecewise constant collocation $ (Q_{N}^{L, 0}) $ method and linear collocation $ (Q_{N}^{L, 1}) $ method, we verified the efficiency of the method through error analysis and numerical examples.","PeriodicalId":48811,"journal":{"name":"Journal of Applied Analysis and Computation","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135106059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
DECAY PROPERTIES AND ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS FOR THE NONLINEAR FRACTIONAL SCHRÖDINGER-POISSON SYSTEM 非线性分数阶schrÖdinger-poisson系统正解的衰减性质及渐近行为
4区 数学
Journal of Applied Analysis and Computation Pub Date : 2023-01-01 DOI: 10.11948/20220378
Lintao Liu, Haibo Chen, Jie Yang
{"title":"DECAY PROPERTIES AND ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS FOR THE NONLINEAR FRACTIONAL SCHRÖDINGER-POISSON SYSTEM","authors":"Lintao Liu, Haibo Chen, Jie Yang","doi":"10.11948/20220378","DOIUrl":"https://doi.org/10.11948/20220378","url":null,"abstract":"In this paper, we study the following nonlinear fractional Schrödinger-Poisson system <p class=\"disp_formula\">$begin{equation*}left{begin{array}{ll}(-Delta)^{s}u+lambda V(x)u+muphi u=|u|^{p-2}u, &amp; hbox{in}; mathbb{R}^3 , (-Delta)^{s}phi=u^{2}, &amp; hbox{in}; mathbb{R}^3, end{array}right.end{equation*}$ where <inline-formula><tex-math id=\"M1\">begin{document}$sin(frac{3}{4}, 1)$end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M2\">begin{document}$ 2<p<4$end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M3\">begin{document}$lambda, mu$end{document}</tex-math></inline-formula> are positive parameters and the potential <inline-formula><tex-math id=\"M4\">begin{document}$V(x)$end{document}</tex-math></inline-formula> is a nonnegative continuous function with a potential well <inline-formula><tex-math id=\"M5\">begin{document}$Omega=int V^{-1}(0)$end{document}</tex-math></inline-formula>. By establishing truncation technique and the parameter-dependent compactness lemma, the existence, decay rate and asymptotic behavior of positive solutions are established. Moreover, we prove some nonexistence results in the case of <inline-formula><tex-math id=\"M6\">begin{document}$ 2<pleq3$end{document}</tex-math></inline-formula>.","PeriodicalId":48811,"journal":{"name":"Journal of Applied Analysis and Computation","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135105890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A STUDY ON STABILITY, BIFURCATION ANALYSIS AND CHAOS CONTROL OF A DISCRETE-TIME PREY-PREDATOR SYSTEM INVOLVING ALLEE EFFECT 考虑狭缝效应的离散食饵-捕食系统的稳定性、分岔分析及混沌控制研究
4区 数学
Journal of Applied Analysis and Computation Pub Date : 2023-01-01 DOI: 10.11948/20220532
Özlem AK GÜMÜŞ
{"title":"A STUDY ON STABILITY, BIFURCATION ANALYSIS AND CHAOS CONTROL OF A DISCRETE-TIME PREY-PREDATOR SYSTEM INVOLVING ALLEE EFFECT","authors":"Özlem AK GÜMÜŞ","doi":"10.11948/20220532","DOIUrl":"https://doi.org/10.11948/20220532","url":null,"abstract":"This paper examines the stability and bifurcation of a discrete-time prey-predator system that is modified by the Allee effect on the prey population. The system undergoes flip and Neimark-Sacker bifurcations in a small neighborhood of the unique positive fixed point depending on the densities of prey-predator. The OGY method and hybrid control method are used to control the chaotic behavior that results from Neimark-Sacker bifurcation. In addition, numerical simulations are performed to illustrate the theoretical results. To keep the ecosystem stable, it is crucial to research how populations of prey and predator interact. The Allee effect is a significant evolutionary force that alters population size by affecting both prey and predator behavior. It would be more realistic to look into population behavior in light of this effect, which results from population density (number of individuals per unit area). The increase in the density of predator in the model with the Allee effect pushes the prey to extinction. When the density of predator is suppressed, the stability continues for a certain time before undergoing bifurcation.","PeriodicalId":48811,"journal":{"name":"Journal of Applied Analysis and Computation","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135106053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
SUCCESSIVE ITERATIONS FOR POSITIVE EXTREMAL SOLUTIONS OF BOUNDARY VALUE PROBLEMS ON THE HALF-LINE 边值问题半线上正极值解的连续迭代
4区 数学
Journal of Applied Analysis and Computation Pub Date : 2023-01-01 DOI: 10.11948/20220531
Siham Ghiatou, John R. Graef, Toufik Moussaoui
{"title":"SUCCESSIVE ITERATIONS FOR POSITIVE EXTREMAL SOLUTIONS OF BOUNDARY VALUE PROBLEMS ON THE HALF-LINE","authors":"Siham Ghiatou, John R. Graef, Toufik Moussaoui","doi":"10.11948/20220531","DOIUrl":"https://doi.org/10.11948/20220531","url":null,"abstract":"The authors study the existence of positive extremal solutions to the differential equation <p class=\"disp_formula\">$ -u''+lambda u=aleft(tright)f(t, u(t)), quad tin I, $ subject to the boundary conditions <p class=\"disp_formula\"><disp-formula> <label/> <tex-math id=\"FE2\"> begin{document}$ uleft(0 right)=uleft(infty right)=0, $end{document} </tex-math></disp-formula> where <inline-formula><tex-math id=\"M1\">begin{document}$ I=(0, infty) $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M2\">begin{document}$ f: mathbb{R^{+}times R^{+}}rightarrow mathbb{R^{+}} $end{document}</tex-math></inline-formula> is continuous, <inline-formula><tex-math id=\"M3\">begin{document}$ a:Irightarrow mathbb{R^{+}} $end{document}</tex-math></inline-formula>, and <inline-formula><tex-math id=\"M4\">begin{document}$ lambda &gt;0 $end{document}</tex-math></inline-formula> is a parameter. Their results are obtained by using the monotone iterative method and are illustrated with an example.","PeriodicalId":48811,"journal":{"name":"Journal of Applied Analysis and Computation","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135105587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
SPREADING SPEED OF A NONLOCAL DIFFUSIVE LOGISTIC MODEL WITH FREE BOUNDARIES IN TIME PERIODIC ENVIRONMENT 时间周期环境下具有自由边界的非局部扩散逻辑模型的扩散速度
4区 数学
Journal of Applied Analysis and Computation Pub Date : 2023-01-01 DOI: 10.11948/20220543
Tong Wang, Binxiang Dai
{"title":"SPREADING SPEED OF A NONLOCAL DIFFUSIVE LOGISTIC MODEL WITH FREE BOUNDARIES IN TIME PERIODIC ENVIRONMENT","authors":"Tong Wang, Binxiang Dai","doi":"10.11948/20220543","DOIUrl":"https://doi.org/10.11948/20220543","url":null,"abstract":"In Zhang, Liu and Zhou [<xref ref-type=\"bibr\" rid=\"b11\">11</xref>], a nonlocal diffusion model with double free boundaries in time periodic environment was introduced and studied. A spreading-vanishing dichotomy is shown to govern the long time dynamical behavior. However, when spreading happens, the spreading speed was left open in [<xref ref-type=\"bibr\" rid=\"b11\">11</xref>]. In this paper, we answer this question. We obtain the spreading speed by solving the associated time periodic semi-wave problems and constructing new upper and lower solutions.","PeriodicalId":48811,"journal":{"name":"Journal of Applied Analysis and Computation","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135105591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
THE SEIR MODEL WITH PULSE AND DIFFUSION OF VIRUS IN THE ENVIRONMENT 具有脉冲和病毒在环境中扩散的seir模型
4区 数学
Journal of Applied Analysis and Computation Pub Date : 2023-01-01 DOI: 10.11948/20230207
Yue Tang, Inkyung Ahn, Zhigui Lin
{"title":"THE SEIR MODEL WITH PULSE AND DIFFUSION OF VIRUS IN THE ENVIRONMENT","authors":"Yue Tang, Inkyung Ahn, Zhigui Lin","doi":"10.11948/20230207","DOIUrl":"https://doi.org/10.11948/20230207","url":null,"abstract":"This paper addresses a reaction-diffusion problem featuring impulsive effects under Neumann boundary conditions. The model simulates the periodic eradication of viruses in an environment. Initially, we establish the well-posedness of the reaction-diffusion model. We define the basic reproduction number $R_0$ for the problem in the absence of pulsing and compute the principal eigenvalue of the corresponding elliptic eigenvalue problem. Utilizing Lyapunov functionals and Green's first identity, we derive the global threshold dynamics of the system. Specifically, when $R_0 < 1$, the disease-free equilibrium is globally asymptotically stable; conversely, if $R_0 > 1$, the system exhibits uniform persistence, and the endemic equilibrium is globally asymptotically stable. Additionally, we consider the generalized principal eigenvalues for the problem with pulsing and provide sufficient conditions for the stability of both the disease-free equilibrium and the positive periodic solution. Finally, we corroborate our theoretical findings through numerical simulations, particularly discussing the impacts of periodic environmental cleaning.","PeriodicalId":48811,"journal":{"name":"Journal of Applied Analysis and Computation","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135105885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR DOUBLE PHASE PROBLEM WITH INDEFINITE SINGULAR TERMS 不定奇异项双相问题正周期解的存在性
4区 数学
Journal of Applied Analysis and Computation Pub Date : 2023-01-01 DOI: 10.11948/20230070
Yu Cheng, Baoyuan Shan, Zhanbing Bai
{"title":"EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR DOUBLE PHASE PROBLEM WITH INDEFINITE SINGULAR TERMS","authors":"Yu Cheng, Baoyuan Shan, Zhanbing Bai","doi":"10.11948/20230070","DOIUrl":"https://doi.org/10.11948/20230070","url":null,"abstract":"In this article, the solvability of a class of periodic boundary value problems with double phase operators and mixed singular terms is considered. By applying the continuation theorem of Manásevich-Mawhin and techniques of a prior estimates, some existence results of positive solutions are obtained. Several numerical examples are given to illustrate the main results.","PeriodicalId":48811,"journal":{"name":"Journal of Applied Analysis and Computation","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135105886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
NEW OPERATIONAL MATRIX OF RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVE OF ORTHONORMAL BERNOULLI POLYNOMIALS FOR THE NUMERICAL SOLUTION OF SOME DISTRIBUTED-ORDER TIME-FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS 一些分布阶时间分数阶偏微分方程数值解的标准正交伯努利多项式riemann-liouville分数阶导数的新运算矩阵
4区 数学
Journal of Applied Analysis and Computation Pub Date : 2023-01-01 DOI: 10.11948/20230039
M. Pourbabaee, A. Saadatmandi
{"title":"NEW OPERATIONAL MATRIX OF RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVE OF ORTHONORMAL BERNOULLI POLYNOMIALS FOR THE NUMERICAL SOLUTION OF SOME DISTRIBUTED-ORDER TIME-FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS","authors":"M. Pourbabaee, A. Saadatmandi","doi":"10.11948/20230039","DOIUrl":"https://doi.org/10.11948/20230039","url":null,"abstract":"In this article, the orthonormal Bernoulli polynomials (OBPs) and their properties are applied for concluding a general technique for forming a new operational matrix of the distributed-order (DO) fractional derivative. Then, we apply tau approach and obtained operational matrix to solve some DO time-fractional partial differential equations including distributed-order Rayleigh-Stokes problem (DRSP) for a generalized second-grade fluid and DO anomalous sub-diffusion equation. Our methodology reduces the solution of these problems to a set of algebraic equations. By analysis the error of approximation by the obtained matrix and comparing between the numerical solutions and exact result, we can conclude that this operational matrix is valid to solve the mentioned equations. Also, to confirm the accuracy and the validity of our technique three examples are provided. Finally, we compare obtained results from this approach with the achieved results from relevant studies.","PeriodicalId":48811,"journal":{"name":"Journal of Applied Analysis and Computation","volume":"142 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135105894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
THE BEST MATCHING PARAMETERS AND NORM CALCULATION OF BOUNDED OPERATORS WITH SUPER-HOMOGENEOUS KERNEL 超齐次核有界算子的最佳匹配参数及范数计算
4区 数学
Journal of Applied Analysis and Computation Pub Date : 2023-01-01 DOI: 10.11948/20230165
Qian Zhao, Yong Hong, Bing He
{"title":"THE BEST MATCHING PARAMETERS AND NORM CALCULATION OF BOUNDED OPERATORS WITH SUPER-HOMOGENEOUS KERNEL","authors":"Qian Zhao, Yong Hong, Bing He","doi":"10.11948/20230165","DOIUrl":"https://doi.org/10.11948/20230165","url":null,"abstract":"The concept of super-homogeneous function is introduced, sufficient and necessary condition for best matching parameters of bounded operator with super-homogeneous kernel is discussed, the norm formula for mutual mapping operators between weighted Lebesgue function space and weighted normed sequence space is obtained, and some special cases are given.","PeriodicalId":48811,"journal":{"name":"Journal of Applied Analysis and Computation","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135106047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A FRACTIONAL LANDWEBER ITERATION METHOD FOR SIMULTANEOUS INVERSION IN A TIME-FRACTIONAL DIFFUSION EQUATION 时间-分数阶扩散方程同时反演的分数阶landweber迭代法
4区 数学
Journal of Applied Analysis and Computation Pub Date : 2023-01-01 DOI: 10.11948/20230051
Jin Wen, Chong-Wang Yue, Zhuan-Xia Liu, Donal O'Regan
{"title":"A FRACTIONAL LANDWEBER ITERATION METHOD FOR SIMULTANEOUS INVERSION IN A TIME-FRACTIONAL DIFFUSION EQUATION","authors":"Jin Wen, Chong-Wang Yue, Zhuan-Xia Liu, Donal O'Regan","doi":"10.11948/20230051","DOIUrl":"https://doi.org/10.11948/20230051","url":null,"abstract":"In the present paper, we study the problem to identify the space-dependent source term and initial value simultaneously for a time-fractional diffusion equation. This inverse problem is ill-posed, and we use the idea of decoupling to turn it into two operator equations based on the Fourier method. To solve the inverse problem, a fractional Landweber regularization method is proposed. Furthermore, we present convergence estimates between the exact solution and the regularized solution by using the a-priori and the a-posteriori parameter choice rules. In order to verify the accuracy and efficiency of the proposed method, several numerical examples are constructed.","PeriodicalId":48811,"journal":{"name":"Journal of Applied Analysis and Computation","volume":"156 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135104296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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