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Computational Methods for Differential Equations最新文献

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A numerical technique for solving nonlinear fractional stochastic integro-differential equations with n-dimensional Wiener process 求解n维Wiener过程的非线性分数阶随机积分微分方程的一种数值方法
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-05 DOI: 10.22034/CMDE.2020.41130.1784
Elnaz Aryani, A. Babaei, Ali Valinejad
{"title":"A numerical technique for solving nonlinear fractional stochastic integro-differential equations with n-dimensional Wiener process","authors":"Elnaz Aryani, A. Babaei, Ali Valinejad","doi":"10.22034/CMDE.2020.41130.1784","DOIUrl":"https://doi.org/10.22034/CMDE.2020.41130.1784","url":null,"abstract":"This paper deals with the numerical solution of nonlinear fractional stochastic integro-differential equations with the n-dimensional Wiener process. A new computational method is employed to approximate the solution of the considered problem. This technique is based on the modified hat functions, the Caputo derivative and a suitable numerical integration rule. Error estimate of the method is investigated in detail. At the end, illustrative examples are included to demonstrate the validity and effectiveness of the presented approach.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45862645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Bounding error of calculating the matrix functions 计算矩阵函数的边界误差
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-05 DOI: 10.22034/CMDE.2020.38964.1708
Marzieh Dehghani-Madiseh
{"title":"Bounding error of calculating the matrix functions","authors":"Marzieh Dehghani-Madiseh","doi":"10.22034/CMDE.2020.38964.1708","DOIUrl":"https://doi.org/10.22034/CMDE.2020.38964.1708","url":null,"abstract":"Matrix functions play important roles in various branches of science and engineering. In numerical computations and physical measurements there are several sources of error which significantly affect the main results obtained from solving the problems. This effect also influences the matrix computations. In this paper, we propose some approaches to enclose the matrix functions. We then present some analytical arguments to ensure that the obtained enclosures contain the exact result. Numerical experiments are given to illustrate the performance and effectiveness of the proposed approaches.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48637753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An infinite number of nonnegative solutions for iterative system of singular fractional order boundary value problems 奇异分数阶边值问题迭代系统的无穷多个非负解
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-03 DOI: 10.22034/CMDE.2020.41028.1780
Khuddush Mahammad, K. R. Prasad, P. Veeraiah
{"title":"An infinite number of nonnegative solutions for iterative system of singular fractional order boundary value problems","authors":"Khuddush Mahammad, K. R. Prasad, P. Veeraiah","doi":"10.22034/CMDE.2020.41028.1780","DOIUrl":"https://doi.org/10.22034/CMDE.2020.41028.1780","url":null,"abstract":"In this paper, we consider the iterative system of singular Rimean-Liouville fractional order boundary value problems with RiemannStieltjes integral boundary conditions involving increasing homeomorphism and positive homomorphism operator(IHPHO). By using Krasnoselskii’s cone fixed point theorem in a Banach space, we derive sufficent conditions for the existence of infinite number of nonnegative solutions. The sufficient conditions are also derived for the existence of unique nonnegative solution to the addressed problem by fixed point theorem in a complete metric space. As an application, we present an example to illustrate the main results.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44387796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Non-uniform L1/DG method for one-dimensional time-fractional convection equation 一维时间分数对流方程的非均匀L1/DG方法
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-03 DOI: 10.22034/CMDE.2020.41761.1805
Zhen Wang
{"title":"Non-uniform L1/DG method for one-dimensional time-fractional convection equation","authors":"Zhen Wang","doi":"10.22034/CMDE.2020.41761.1805","DOIUrl":"https://doi.org/10.22034/CMDE.2020.41761.1805","url":null,"abstract":"In this paper, we present an efficient numerical method to solve a one-dimensional time-fractional convection equation whose solution has a certain weak regularity at the starting time, where the time-fractional derivative in the Caputo sense with order in (0,1) is discretized by the L1 finite difference method on non-uniform meshes and the spatial derivative by the discontinuous Galerkin (DG) finite element method. The stability and convergence of the method are analyzed. Numerical experiments are provided to confirm the theoretical results.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44163359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The Symmetry Analysis and Analytical Studies of the Rotational Green-Naghdi (R-GN) Equation 转动Green-Naghdi (R-GN)方程的对称性分析及解析研究
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-03 DOI: 10.22034/CMDE.2020.41145.1785
Zehra Pinar
{"title":"The Symmetry Analysis and Analytical Studies of the Rotational Green-Naghdi (R-GN) Equation","authors":"Zehra Pinar","doi":"10.22034/CMDE.2020.41145.1785","DOIUrl":"https://doi.org/10.22034/CMDE.2020.41145.1785","url":null,"abstract":"The simplified phenomenological model of long-crested shallow-water wave propagations is considered without/with the Coriolis effect. Symmetry analysis is taken into consideration to obtain exact solutions. Both classical wave transformation and transformations are obtained with symmetries and solvable equations are kept thanks to these transformations. Additionally, the exact solutions are obtained via various methods which are ansatz based methods. The obtained results have a major role in the literature so that the considered equation is seen in a large scale of applications in the area of geophysical.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43341043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Finite Volume Element Approximation For Time-dependent Convection-Diffusion-ReactionEquations With Memory 具有记忆的时变对流-扩散-反应方程的有限体积元逼近
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-03 DOI: 10.22034/CMDE.2020.30193.1447
Anas Rachid, M. Bahaj, R. Fakhar
{"title":"Finite Volume Element Approximation For Time-dependent Convection-Diffusion-ReactionEquations With Memory","authors":"Anas Rachid, M. Bahaj, R. Fakhar","doi":"10.22034/CMDE.2020.30193.1447","DOIUrl":"https://doi.org/10.22034/CMDE.2020.30193.1447","url":null,"abstract":"Error estimates for element schemes for time-dependent for convection-diffusion-reaction equations with memory are derived and stated. For the spatially discrete scheme, optimal order error estimates in $L^{2},$ $H^{1}, $ and $W^{1,p }$ norms for $2leq p <infty ,$ are obtained. Inthis paper, we also study the lumped mass modification. Based on the Crank-Nicolson method, a time discretization scheme is discussed and related error estimates are derived.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45589537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Dynamical behaviours of Bazykin-Berezovskaya model with fractional-order and its discretization 分数阶Bazykin-Berezovskaya模型的动力学行为及其离散化
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-03 DOI: 10.22034/CMDE.2020.30802.1460
M. H. Akrami
{"title":"Dynamical behaviours of Bazykin-Berezovskaya model with fractional-order and its discretization","authors":"M. H. Akrami","doi":"10.22034/CMDE.2020.30802.1460","DOIUrl":"https://doi.org/10.22034/CMDE.2020.30802.1460","url":null,"abstract":"‎This paper is devoted to study dynamical behaviours of the fractional-order Bazykin-Berezovskaya model and its discretization‎. ‎The fractional derivative has been described in the Caputo sense‎. ‎We show that the discretized system‎, ‎exhibits more complicated dynamical behaviours than its corresponding fractional-order model‎. ‎Specially‎, ‎in the discretized model Neimark-Sacker and flip bifurcations and also chaos phenomena will happen‎. ‎In the final part‎, ‎some numerical simulation verify the analytical results‎.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48332087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Toward a new understanding of cohomological method for fractional partial differential equations 对分数阶偏微分方程上同调方法的新认识
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-02 DOI: 10.22034/CMDE.2020.39020.1710
A. D. Nezhad, M. Moghaddam
{"title":"Toward a new understanding of cohomological method for fractional partial differential equations","authors":"A. D. Nezhad, M. Moghaddam","doi":"10.22034/CMDE.2020.39020.1710","DOIUrl":"https://doi.org/10.22034/CMDE.2020.39020.1710","url":null,"abstract":"One of the aims of this article is to investigate the solvability and unsolvability conditions for fractional cohomological equation‎ ‎$ psi^{alpha} f=g $‎, ‎on‎ ‎$ mathbb{T}^n $‎. ‎We prove that if‎ ‎$ f $‎ ‎is not analytic‎, ‎then fractional integro-differential equation‎ ‎$ I_t^{1-alpha} D_x^{alpha}u(x,t)+i I_x^{1-alpha} D_t^{alpha}u(x,t)=f(t) $‎ ‎has no solution in‎ ‎$ C^1(B) $ with $0< alpha leq 1$‎. ‎‎W‎e ‎also‎ obtain ‎solutions ‎for‎ the space-time fractional heat ‎equations‎ on‎ ‎$ mathbb{S}^1 $‎ ‎and ‎$ mathbb{T}^n $‎. ‎At the end of this article‎, ‎there are examples of fractional partial differential equations and a fractional integral equation together with their solutions‎.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43070857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Second Order Boundary Value Problems of Nonsingular Type on Time Scales 时间尺度上的非奇异型二阶边值问题
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-02 DOI: 10.22034/CMDE.2020.24117.1294
F. Topal, Buse Eralp
{"title":"Second Order Boundary Value Problems of Nonsingular Type on Time Scales","authors":"F. Topal, Buse Eralp","doi":"10.22034/CMDE.2020.24117.1294","DOIUrl":"https://doi.org/10.22034/CMDE.2020.24117.1294","url":null,"abstract":"In this study, existence of positive solutions are considered for second order boundary value problems on any time scales even in the case when y =0 may also be a solution.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47412146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
PDE-based hyperbolic-parabolic model for image denoising with forward-backward diffusivity 基于PDE的双曲-抛物型前向扩散图像去噪模型
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-02 DOI: 10.22034/CMDE.2020.37139.1646
Santosh Kumar, Khursheed Alam
{"title":"PDE-based hyperbolic-parabolic model for image denoising with forward-backward diffusivity","authors":"Santosh Kumar, Khursheed Alam","doi":"10.22034/CMDE.2020.37139.1646","DOIUrl":"https://doi.org/10.22034/CMDE.2020.37139.1646","url":null,"abstract":"In the present study, we propose an effective nonlinear anisotropic diffusion-based hyperbolic parabolic model for image denoising and edge detection. The hyperbolic-parabolic model employs a second-order PDEs and have a second-time derivative to time t. This approach is very effective to preserve sharper edges and better-denoised images of noisy images. Our model is well-posed and it has a unique weak solution under certain conditions, which is obtained by using an iterative finite difference explicit scheme. The results are obtained in terms of peak signal to noise ratio (PSNR) as a metric, using an explicit scheme with forward-backward diffusivities.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49134427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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