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Computational Methods for Differential Equations最新文献

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Solving Optimal Control Problems by using Hermite polynomials 用Hermite多项式求解最优控制问题
IF 1.1
Computational Methods for Differential Equations Pub Date : 2020-04-01 DOI: 10.22034/CMDE.2020.29747.1433
A. Yari, M. Mirnia
{"title":"Solving Optimal Control Problems by using Hermite polynomials","authors":"A. Yari, M. Mirnia","doi":"10.22034/CMDE.2020.29747.1433","DOIUrl":"https://doi.org/10.22034/CMDE.2020.29747.1433","url":null,"abstract":"‎In this paper‎, ‎one numerical method is presented for numerical approximation of linear constrained optimal control problems with quadratic performance index‎. ‎The method with variable coefficients is based on Hermite polynomials‎. ‎The properties of Hermite polynomials with the operational matrices of derivative are used to reduce optimal control problems to the solution of linear algebraic equations‎. ‎Illustrative examples are included to demonstrate the validity and applicability of the technique‎.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":"8 1","pages":"314-329"},"PeriodicalIF":1.1,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49492379","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: 4
Application of spline to approximate the solution of singularly perturbed boundary-value problems 样条函数在奇异摄动边值问题近似解中的应用
IF 1.1
Computational Methods for Differential Equations Pub Date : 2020-04-01 DOI: 10.22034/CMDE.2020.30331.1449
K. Farajeyan, J. Rashidinia, R. Jalilian, N. Maleki
{"title":"Application of spline to approximate the solution of singularly perturbed boundary-value problems","authors":"K. Farajeyan, J. Rashidinia, R. Jalilian, N. Maleki","doi":"10.22034/CMDE.2020.30331.1449","DOIUrl":"https://doi.org/10.22034/CMDE.2020.30331.1449","url":null,"abstract":"We develop a class of new methods based on modification of polynomial spline function for the numerical solution of singularly perturbed boundary-value problems. The modified spline contains the exponential terms and named by tension spline, which is infinity smooth. Tension spline contain parameter, by choosing arbitrary values of such parameters the various classes of spline can be obtained. The proposed methods are accurate for solution of linear and non-linear singularly perturbed boundary-value problems. Boundary formulas are developed to associate with spline methods. These methods are converging. The analysis of convergence is shown to yield up to O(h^8 ) approximation to the solution of singularly perturbed boundary-value problems. Comparison are carried out, numerical examples are given to showing the efficiency of our methods","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":"8 1","pages":"373-388"},"PeriodicalIF":1.1,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45286645","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
On the travelling wave solutions of Ostrovsky equation 关于Ostrovsky方程的行波解
IF 1.1
Computational Methods for Differential Equations Pub Date : 2020-04-01 DOI: 10.22034/CMDE.2020.30047.1445
S. Demiray, H. Bulut
{"title":"On the travelling wave solutions of Ostrovsky equation","authors":"S. Demiray, H. Bulut","doi":"10.22034/CMDE.2020.30047.1445","DOIUrl":"https://doi.org/10.22034/CMDE.2020.30047.1445","url":null,"abstract":"In this paper, extended trial equation method (ETEM) is applied to find exact solutions of (1+1) dimensional nonlinear Ostrovsky equation. We constitute some exact solutions such as soliton solutions, rational, Jacobi elliptic and hyperbolic function solutions of this equation via ETEM. Then, we submit the results obtained by using this method.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":"8 1","pages":"401-407"},"PeriodicalIF":1.1,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48409285","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
Interval extensions of the Halley method and its modified method for finding enclosures of roots of nonlinear equations 求非线性方程根围合的Halley方法的区间扩展及其修正方法
IF 1.1
Computational Methods for Differential Equations Pub Date : 2020-04-01 DOI: 10.22034/CMDE.2020.25755.1320
Tahereh Eftekhari
{"title":"Interval extensions of the Halley method and its modified method for finding enclosures of roots of nonlinear equations","authors":"Tahereh Eftekhari","doi":"10.22034/CMDE.2020.25755.1320","DOIUrl":"https://doi.org/10.22034/CMDE.2020.25755.1320","url":null,"abstract":"In this paper, interval extensions of the Halley method and its modified method for finding enclosures of roots of nonlinear equations are produced. Error analysis and convergence will be discussed. Also, these methods are compared together with the interval Newton method.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":"8 1","pages":"222-235"},"PeriodicalIF":1.1,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48789442","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
Distribution of zeros of solutions of sixth order (2 ≤ n ≤ 5)-points boundary value problem in terms of semi-critical intervals 半临界区间六阶(2≤n≤5)点边值问题解的零点分布
IF 1.1
Computational Methods for Differential Equations Pub Date : 2020-04-01 DOI: 10.22034/CMDE.2020.28205.1384
Salah Ali Saleh Al-Joufi, K. Jwamer
{"title":"Distribution of zeros of solutions of sixth order (2 ≤ n ≤ 5)-points boundary value problem in terms of semi-critical intervals","authors":"Salah Ali Saleh Al-Joufi, K. Jwamer","doi":"10.22034/CMDE.2020.28205.1384","DOIUrl":"https://doi.org/10.22034/CMDE.2020.28205.1384","url":null,"abstract":"In this paper, the issue of distribution of zeros of the solutions of linear homogenous differential equations (LHDE) have been investigated in terms of semi-critical intervals. We shall follow a geometric approach to state and prove some properties of LHDEs of the sixth order with (2, 3, 4, and 5 points) boundary conditions and with measurable coefficients. Moreover, the relations between semi-critical intervals of the LHDEs have been explored. Also, the obtained results have been generalized for the 5th order differential equations.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":"8 1","pages":"294-304"},"PeriodicalIF":1.1,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49112054","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
Solving Stiff Systems by using Symbolic - Numerical Method 用符号-数值方法求解刚性系统
IF 1.1
Computational Methods for Differential Equations Pub Date : 2020-04-01 DOI: 10.22034/CMDE.2020.28834.1401
M. Mirkarim, Abdolali Basiri, S. Rahmany
{"title":"Solving Stiff Systems by using Symbolic - Numerical Method","authors":"M. Mirkarim, Abdolali Basiri, S. Rahmany","doi":"10.22034/CMDE.2020.28834.1401","DOIUrl":"https://doi.org/10.22034/CMDE.2020.28834.1401","url":null,"abstract":"In this paper, an efficient symbolic-numerical procedure based on the power series method is presented for solving a system of differential equations. The basic idea is to substitute power series into the differential equations and to find a polynomial system of coefficients, where a powerful symbolic computation technique (i.e., Grobner basis) is used to solve the system. In fact, the proposed method is an excellent bridge between symbolic and numeric computation and specially, enables us to find the solution of linear and non-linear stiff systems. Numerical experiments were performed to justify our new approach.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":"8 1","pages":"282-293"},"PeriodicalIF":1.1,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49559398","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
Group-invariant solutions for time-fractional Fornberg-Whitham equation by Lie symmetry analysis 李对称性分析法求解时间分数阶Fornberg-Whitham方程的群不变解
IF 1.1
Computational Methods for Differential Equations Pub Date : 2020-04-01 DOI: 10.22034/CMDE.2020.27299.1362
R. Najafi
{"title":"Group-invariant solutions for time-fractional Fornberg-Whitham equation by Lie symmetry analysis","authors":"R. Najafi","doi":"10.22034/CMDE.2020.27299.1362","DOIUrl":"https://doi.org/10.22034/CMDE.2020.27299.1362","url":null,"abstract":"This paper is concerned with the time-fractional Fornberg-Whitham equation using Lie symmetry analysis. This equation is used to describe the physical processes of models possessing memory. By employing the classical and nonclassical Lie symmetry analysis, the invariance properties of this equation are investigated. The similarity reductions and new exact solutions are obtained.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":"8 1","pages":"251-258"},"PeriodicalIF":1.1,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45894614","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: 3
Solving one dimensional nonlinear coupled Burger’s equations using high accuracy multiquadric quasi-interpolation 高精度二次拟插值法求解一维非线性耦合Burger方程
IF 1.1
Computational Methods for Differential Equations Pub Date : 2020-04-01 DOI: 10.22034/CMDE.2020.32252.1504
M. Rahimi, H. Adibi
{"title":"Solving one dimensional nonlinear coupled Burger’s equations using high accuracy multiquadric quasi-interpolation","authors":"M. Rahimi, H. Adibi","doi":"10.22034/CMDE.2020.32252.1504","DOIUrl":"https://doi.org/10.22034/CMDE.2020.32252.1504","url":null,"abstract":"In this paper a multiquadric quasi-interpolation (MQQI) scheme for solving the system of 1-D coupled nonlinear Burger’s equations (CNBE) is presented. The scheme utilizes the derivative of the quasi-interpolation for approximating the spatial derivative and the Taylor series expansion for temporal derivatives. Simulations are presented to demonstrate the efficiency and applicability of the scheme. Also, we have shown that our scheme is superior to some numerical schemes already done.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":"8 1","pages":"347-363"},"PeriodicalIF":1.1,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49130075","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 efficient method to approximate eigenvalues and eigenfunctions of high order Sturm-Liouville problems 高阶Sturm-Liouville问题特征值和特征函数的一种有效逼近方法
IF 1.1
Computational Methods for Differential Equations Pub Date : 2020-04-01 DOI: 10.22034/CMDE.2020.29144.1417
J. Biazar, M. Dehghan, T. Houlari
{"title":"An efficient method to approximate eigenvalues and eigenfunctions of high order Sturm-Liouville problems","authors":"J. Biazar, M. Dehghan, T. Houlari","doi":"10.22034/CMDE.2020.29144.1417","DOIUrl":"https://doi.org/10.22034/CMDE.2020.29144.1417","url":null,"abstract":"determination of eigenvalues and eigenfunctions of a High-order Sturm-Liouville problem (HSLP) is considered. To this end, the Differential Transformation Method (DTM) is applied which is an efficient technique for solving differential equations. The results of the proposed approach are compared with those of some well-known methods reported in the literature. Four illustrative real life examples of mechanical engineering are provided to show the ability and the cost-effectiveness of this numerical approach.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":"8 1","pages":"389-400"},"PeriodicalIF":1.1,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43373051","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 numerical method based on the moving mesh for the solving of a mathematical model of the avascular tumor growth 基于运动网格的无血管肿瘤生长数学模型的数值求解方法
IF 1.1
Computational Methods for Differential Equations Pub Date : 2020-03-14 DOI: 10.22034/CMDE.2020.31455.1472
A. Soheili, Mina Bagherpoorfard
{"title":"A numerical method based on the moving mesh for the solving of a mathematical model of the avascular tumor growth","authors":"A. Soheili, Mina Bagherpoorfard","doi":"10.22034/CMDE.2020.31455.1472","DOIUrl":"https://doi.org/10.22034/CMDE.2020.31455.1472","url":null,"abstract":"Using adaptive mesh methods is one of the strategies to improve numerical solutions in time-dependent partial differential equations. The moving mesh method is an adaptive mesh method, which, firstly does not need an increase in the number of mesh points, secondly reduces the concentration of points in the steady areas of the solutions that do not need a high degree of accuracy, and finally places the points in the areas, where a high degree of accuracy is needed. In this paper, we improved the numerical solutions for a three-phase model of avascular tumor growth by using the moving mesh method. The physical formulation of this model uses reaction-diffusion dynamics with the mass conservation law and appears in the format of the nonlinear system of partial differential equations based on the continuous density of three proliferating, quiescent, and necrotic cell categorizations. Our numerical results show more accurate numerical solutions, as compared to the corresponding fixed mesh method. Moreover, this method leads to the higher order of numerical convergence.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45211508","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
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