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Computational Methods for Differential Equations最新文献

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Numerical solution of space fractional diffusion equation using shifted Gegenbauer polynomials 用移位Gegenbauer多项式求解空间分数阶扩散方程
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-05 DOI: 10.22034/CMDE.2020.42106.1818
K. Issa, B. Yisa, J. Biazar
{"title":"Numerical solution of space fractional diffusion equation using shifted Gegenbauer polynomials","authors":"K. Issa, B. Yisa, J. Biazar","doi":"10.22034/CMDE.2020.42106.1818","DOIUrl":"https://doi.org/10.22034/CMDE.2020.42106.1818","url":null,"abstract":"This paper is concerned with numerical approach for solving space fractional diffusion equation using shifted Gegenbauer polynomials, where the fractional derivatives are expressed in Caputo sense. The properties of Gegenbauer polynomials are exploited to reduce space fractional diffusion equation to a system of ordinary differential equations, that are then solved using finite difference method. Some selected numerical simulations of space fractional diffusion equations are presented and the results are compared with the exact solution, also with the results obtained via other methods in the literature. The comparison reveals that the proposed method is reliable, effective and accurate. All the computations were carried out using Matlab package.","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":"48587365","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
An interval version of the Kuntzmann-Butcher method for solving the initial value problem 求解初值问题的区间型Kuntzmann-Butcher方法
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-05 DOI: 10.22034/CMDE.2020.39203.1720
A. Marciniak, B. Szyszka, Tomasz Hoffmann
{"title":"An interval version of the Kuntzmann-Butcher method for solving the initial value problem","authors":"A. Marciniak, B. Szyszka, Tomasz Hoffmann","doi":"10.22034/CMDE.2020.39203.1720","DOIUrl":"https://doi.org/10.22034/CMDE.2020.39203.1720","url":null,"abstract":"The Kutzmann-Butcher method is the unique implicit four-stage Runge-Kutta method of order 8. In many problems in ordinary differential equations this method realized in floating-point arithmetic gives quite good approximations to the exact solutions, but the results obtained do not contain any information on rounding errors, representation errors and the error of the method. Thus, we describe an interval version of this method, which realized in floating-point interval arithmetic gives approximations (enclosures in the form of interval) containing all these errors. The described method can also include data uncertainties in the intervals obtained.","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":"49254644","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
Design of Normal distribution-based algorithm for solving systems of nonlinear equations 基于正态分布的非线性方程组求解算法设计
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-05 DOI: 10.22034/CMDE.2020.37474.1658
Amir Khakbaz
{"title":"Design of Normal distribution-based algorithm for solving systems of nonlinear equations","authors":"Amir Khakbaz","doi":"10.22034/CMDE.2020.37474.1658","DOIUrl":"https://doi.org/10.22034/CMDE.2020.37474.1658","url":null,"abstract":"In this paper, a completely new statistical based approach is developed for solving the system of nonlinear equations. The developed approach utilizes the characteristics of the normal distribution to search the solution space. The normal distribution is generally introduced by two parameters, i.e., mean and standard deviation. In the developed algorithm, large values of standard deviation enable the algorithm to escape from a local optimum, and small values of standard deviation help the algorithm to find the global optimum. In the following, six benchmark tests and thirteen benchmark case problems are investigated to evaluate the performance of the Normal Distribution-based Algorithm (NDA). The obtained statistical results of NDA are compared with those of PSO, ICA, CS, and ACO. Based on the obtained results, NDA is the least time-consuming algorithm that gets high-quality solutions. Furthermore, few input parameters and simple structure introduce NDA as a user friendly and easy-to-understand algorithm.","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":"49330198","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
Controllability and observability of linear impulsive differential algebraic system with Caputo fractional derivative 具有Caputo分数导数的线性脉冲微分代数系统的能控性和可观测性
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-05 DOI: 10.22034/CMDE.2020.39372.1724
C. Tunç, A. Zehra, Awais Younas
{"title":"Controllability and observability of linear impulsive differential algebraic system with Caputo fractional derivative","authors":"C. Tunç, A. Zehra, Awais Younas","doi":"10.22034/CMDE.2020.39372.1724","DOIUrl":"https://doi.org/10.22034/CMDE.2020.39372.1724","url":null,"abstract":"Linear impulsive fractional differential-algebraic systems (LIFDAS) in a finite-dimensional space are studied. We obtain the solution of LIFDAS. Using Gramian matrices, necessary and sufficient conditions for controllability and observability of time-varying LIFDAS are established. We acquired criterion for time-invariant LIFDAS in the form of rank conditions. The results are more generalized than the results that are obtained for various differential-algebraic systems without impulses","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":"47379880","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
New optical soliton solutions for the thin-film ferroelectric materials equation instead of the numerical solution 薄膜铁电材料方程的新光孤子解代替数值解
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-05 DOI: 10.22034/CMDE.2020.38121.1677
A. Bekir, M. Shehata, E. Zahran
{"title":"New optical soliton solutions for the thin-film ferroelectric materials equation instead of the numerical solution","authors":"A. Bekir, M. Shehata, E. Zahran","doi":"10.22034/CMDE.2020.38121.1677","DOIUrl":"https://doi.org/10.22034/CMDE.2020.38121.1677","url":null,"abstract":"In this article, we will implement the (G′/G)-expansion method which is used for the first time to obtain new optical soliton solutions of the thin-film ferroelectric materials equation (TFFME). Also, the numerical solutions of the suggested equation according to the variational iteration method (VIM) are demonstrated effectively. A comparison between the achieved exact and numerical solutions has been established successfully.","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":"46170581","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: 16
Some new soliton solutions for the nonlinear the fifth-order integrable equations 非线性五阶可积方程的一些新的孤子解
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-05 DOI: 10.22034/CMDE.2020.30833.1462
M. Lakestani, J. Manafian, A. Najafizadeh, Mohammad Partohaghighi
{"title":"Some new soliton solutions for the nonlinear the fifth-order integrable equations","authors":"M. Lakestani, J. Manafian, A. Najafizadeh, Mohammad Partohaghighi","doi":"10.22034/CMDE.2020.30833.1462","DOIUrl":"https://doi.org/10.22034/CMDE.2020.30833.1462","url":null,"abstract":"In this work, we established some exact solutions for the (1 + 1)-dimensional and (2 + 1)-dimensional fifth-order integrable equations ((1+1)D and (2+1)D FOIEs) which is considered based on the improved tanh(ϕ(ξ)/2)-expansion method (IThEM), by utilizing Maple software. We obtained new periodic solitary wave solutions. The obtained solutions include soliton, periodic, kink, kink-singular wave solutions. Comparing our new results with Wazwaz results, namely, Hereman-Nuseri method [2, 3] show that our results give the further solutions. Many other such types of nonlinear equations arising in uid dynamics, plasma physics and nonlinear physics.","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":"43652187","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
Synchronization between Integer & Fractional Chaotic Systems Via. Tracking Control & Non Linear Control With Application 整数与分数阶混沌系统的同步。跟踪控制与非线性控制及其应用
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-05 DOI: 10.22034/CMDE.2020.40144.1750
P. Trikha, L. S. Jahanzaib, T. Khan
{"title":"Synchronization between Integer & Fractional Chaotic Systems Via. Tracking Control & Non Linear Control With Application","authors":"P. Trikha, L. S. Jahanzaib, T. Khan","doi":"10.22034/CMDE.2020.40144.1750","DOIUrl":"https://doi.org/10.22034/CMDE.2020.40144.1750","url":null,"abstract":"In this paper the synchronization between complex fractional order chaotic system and integer order hyper chaotic system has been investigated. Due to increased complexity and presence of additional variables, it seems to be very interesting and can be associated with real life problems. Based on the idea of tracking control and non linear control, we have designed the controllers to obtain the synchronization between the chaotic systems. To establish the efficacy of the methods computations have been carried out. Excellent agreement between the analytical and computational studies has been observed. The achieved synchronization is illustrated in field of secure communication. The results have been compared with published literature.","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":"49183256","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
An Exponential Cubic B-spline Algorithm for the Nonlinear Coupled Burgers' Equation 非线性耦合Burgers方程的指数三次B样条算法
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-05 DOI: 10.22034/CMDE.2020.39486.1727
Ozlem Ersoy Hepson, I. Dag
{"title":"An Exponential Cubic B-spline Algorithm for the Nonlinear Coupled Burgers' Equation","authors":"Ozlem Ersoy Hepson, I. Dag","doi":"10.22034/CMDE.2020.39486.1727","DOIUrl":"https://doi.org/10.22034/CMDE.2020.39486.1727","url":null,"abstract":"The collocation method based on the exponential cubic B-splines (ECB-splines) together with the Crank-Nicolson formula is used to solve nonlinear coupled Burgers' equation (CBE). This method is tested by studying three different problems. The proposed scheme is compared with some existing methods. textbf{It produced accurate results }with the suitable selection of the free parameter of the ECB-spline function. It produces accurate results. Stability of the fully discretized CBE is investigated by the Von Neumann analysis.","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":"49217948","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
A new numerical fractional differentiation formula to approximate the Caputo-Fabrizio fractional derivative: error analysis and stability 一个新的近似Caputo-Fabrizio分数导数的数值分数微分公式：误差分析和稳定性
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-05 DOI: 10.22034/CMDE.2020.37595.1664
Leila Moghadam Dizaj Herik, M. Javidi, M. Shafiee
{"title":"A new numerical fractional differentiation formula to approximate the Caputo-Fabrizio fractional derivative: error analysis and stability","authors":"Leila Moghadam Dizaj Herik, M. Javidi, M. Shafiee","doi":"10.22034/CMDE.2020.37595.1664","DOIUrl":"https://doi.org/10.22034/CMDE.2020.37595.1664","url":null,"abstract":"In the present work, first of all, a new numerical fractional differentiation formula (called the CF2 formula) to approximate the Caputo-Fabrizio fractional derivative of order $alpha,$ $(0<alpha<1)$ is developed. It is established by means of the quadratic interpolation approximation using three points $ (t_{j-2},y(t_{j-2}))$,  $(t_{j-1},y(t_{j-1})) $ and $ (t_{j},y(t_{j})) $ on each interval $[t_{j-1},t_{j}]$ for $ ( j geq 2 )$, while the linear interpolation approximation is applied on the first interval $[t_{0},t_{1}]$. As a result, the new formula can be formally viewed as a modification of the classical CF1 formula, which is obtained by the piecewise linear approximation for $y(t)$. Both the computational efficiency and numerical accuracy of the new formula is superior to that of the CF1 formula. The coefficients and truncation errors of this formula are discussed in detail. {Two test example show} the numerical accuracy of the CF2 formula. The CF1 formula demonstrates that the new CF2 is much more effective and more accurate than the CF1 when solving fractional differential equations. Detailed stability analysis and region stability of the CF2 are also carefully investigated.","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":"44371333","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
Existence and Hyers-Ulam stability of random impulsive stochastic functional integrodifferential equations with finite delays 有限时滞随机脉冲泛函积分微分方程的存在性及Hyers-Ulam稳定性
IF 1.1
Computational Methods for Differential Equations Pub Date : 2021-01-05 DOI: 10.22034/CMDE.2020.32591.1512
A. Anguraj, K. Ramkumar, K. Ravikumar
{"title":"Existence and Hyers-Ulam stability of random impulsive stochastic functional integrodifferential equations with finite delays","authors":"A. Anguraj, K. Ramkumar, K. Ravikumar","doi":"10.22034/CMDE.2020.32591.1512","DOIUrl":"https://doi.org/10.22034/CMDE.2020.32591.1512","url":null,"abstract":"In this article, we concentrate on the existence and Hyers-Ulam stability of random impulsive stochastic functional integrodifferential equations with finite delays. Initially, the existence of the mild solutions to the equations by utilizing Banach fixed point theorem is demonstrated. In the later case we explore the Hyers Ulam stability results under the Lipschitz condition on a bounded and closed interval.","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":"47143702","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
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