Pub Date : 2012-12-06DOI: 10.1590/S1807-03022012000300002
Y. Chalco-Cano, A. Flores-Franulic, H. Román-Flores
The present paper is devoted to obtaining some Ostrowski type inequalities for interval-valued functions. In this context we use the generalized Hukuhara derivative for interval-valued functions. Also some examples and consequences are presented. Mathematical subject classification: Primary: 26E25; Secondary: 35A23.
{"title":"Ostrowski type inequalities for interval-valued functions using generalized Hukuhara derivative","authors":"Y. Chalco-Cano, A. Flores-Franulic, H. Román-Flores","doi":"10.1590/S1807-03022012000300002","DOIUrl":"https://doi.org/10.1590/S1807-03022012000300002","url":null,"abstract":"The present paper is devoted to obtaining some Ostrowski type inequalities for interval-valued functions. In this context we use the generalized Hukuhara derivative for interval-valued functions. Also some examples and consequences are presented. Mathematical subject classification: Primary: 26E25; Secondary: 35A23.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"28 1","pages":"457-472"},"PeriodicalIF":2.6,"publicationDate":"2012-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83681531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-12-06DOI: 10.1590/S1807-03022012000300007
Igor Leite Freire
In this paper it is shown that the inviscid Burgers equation is nonlinearly self-adjoint. Then, from Ibragimov's theorem on conservation laws, local conserved quantities are obtained. Mathematical subject classification: Primary: 76M60; Secondary: 58J70.
{"title":"New conservation laws for inviscid Burgers equation","authors":"Igor Leite Freire","doi":"10.1590/S1807-03022012000300007","DOIUrl":"https://doi.org/10.1590/S1807-03022012000300007","url":null,"abstract":"In this paper it is shown that the inviscid Burgers equation is nonlinearly self-adjoint. Then, from Ibragimov's theorem on conservation laws, local conserved quantities are obtained. Mathematical subject classification: Primary: 76M60; Secondary: 58J70.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"13 1","pages":"559-567"},"PeriodicalIF":2.6,"publicationDate":"2012-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78408022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-11-12DOI: 10.1590/S1807-03022012000300001
F. Ghomanjani, M. H. Farahi, M. Gachpazan
A computational method based on Bezier control points is presented to solve optimal control problems governed by time varying linear dynamical systems subject to terminal state equality constraints and state inequality constraints. The method approximates each of the system state variables and each of the control variables by a Bezier curve of unknown control points. The new approximated problems converted to a quadratic programming problem which can be solved more easily than the original problem. Some examples are given to verify the efficiency and reliability of the proposed method. Mathematical subject classification: 49N10.
{"title":"Bézier control points method to solve constrained quadratic optimal control of time varying linear systems","authors":"F. Ghomanjani, M. H. Farahi, M. Gachpazan","doi":"10.1590/S1807-03022012000300001","DOIUrl":"https://doi.org/10.1590/S1807-03022012000300001","url":null,"abstract":"A computational method based on Bezier control points is presented to solve optimal control problems governed by time varying linear dynamical systems subject to terminal state equality constraints and state inequality constraints. The method approximates each of the system state variables and each of the control variables by a Bezier curve of unknown control points. The new approximated problems converted to a quadratic programming problem which can be solved more easily than the original problem. Some examples are given to verify the efficiency and reliability of the proposed method. Mathematical subject classification: 49N10.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"27 1","pages":"433-456"},"PeriodicalIF":2.6,"publicationDate":"2012-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83047904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-28DOI: 10.1590/S1807-03022012000200005
S. Yazdani, M. Hadizadeh
In this paper, we compute piecewise constant bounds on the solution of mixed nonlinear Volterra-Fredholm integral equations. The enclosures are in the form of intervals which are guaranteed to contain the exact solution considering all round-off and truncation errors, so the width of interval solutions allows us to control the error estimation. An iterative algorithm to improve the accuracy of initial enclosures is given and its convergence are also investigated. Our numerical experiments show that the precision of interval solutions are reasonable in comparison to the classical methods and the obtained conditions and initial enclosure of the proposed algorithm are not restrictive. Mathematical subject classification: 65G20, 45G10, 65G40.
{"title":"Piecewise constant bounds for the solution of nonlinear Volterra-Fredholm integral equations","authors":"S. Yazdani, M. Hadizadeh","doi":"10.1590/S1807-03022012000200005","DOIUrl":"https://doi.org/10.1590/S1807-03022012000200005","url":null,"abstract":"In this paper, we compute piecewise constant bounds on the solution of mixed nonlinear Volterra-Fredholm integral equations. The enclosures are in the form of intervals which are guaranteed to contain the exact solution considering all round-off and truncation errors, so the width of interval solutions allows us to control the error estimation. An iterative algorithm to improve the accuracy of initial enclosures is given and its convergence are also investigated. Our numerical experiments show that the precision of interval solutions are reasonable in comparison to the classical methods and the obtained conditions and initial enclosure of the proposed algorithm are not restrictive. Mathematical subject classification: 65G20, 45G10, 65G40.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"26 1","pages":"305-322"},"PeriodicalIF":2.6,"publicationDate":"2012-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79782475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-28DOI: 10.1590/S1807-03022012000200011
Xiaojing Zhu, D. Pu
A new trust-region SQP method for equality constrained optimization is considered. This method avoids using a penalty function or a filter, and yet can be globally convergent to first-order critical points under some reasonable assumptions. Each SQP step is composed of a normal step and a tangential step for which different trust regions are applied in the spirit of Gould and Toint [Math. Program., 122 (2010), pp. 155-196]. Numerical results demonstrate that this new approach is potentially useful. Mathematical subject classification: 65K05, 90C30, 90C55.
提出了求解等式约束优化问题的一种新的信任域SQP方法。该方法避免了使用惩罚函数或滤波器，并且在合理的假设下可以全局收敛到一阶临界点。每个SQP步骤由一个正规步骤和一个切向步骤组成，根据Gould和Toint [Math]的精神，对这些步骤应用不同的信任区域。程序。， 122 (2010)， pp. 155-196]。数值结果表明，该方法具有潜在的实用价值。数学学科分类:65K05、90C30、90C55。
{"title":"A new double trust regions SQP method without a penalty function or a filter","authors":"Xiaojing Zhu, D. Pu","doi":"10.1590/S1807-03022012000200011","DOIUrl":"https://doi.org/10.1590/S1807-03022012000200011","url":null,"abstract":"A new trust-region SQP method for equality constrained optimization is considered. This method avoids using a penalty function or a filter, and yet can be globally convergent to first-order critical points under some reasonable assumptions. Each SQP step is composed of a normal step and a tangential step for which different trust regions are applied in the spirit of Gould and Toint [Math. Program., 122 (2010), pp. 155-196]. Numerical results demonstrate that this new approach is potentially useful. Mathematical subject classification: 65K05, 90C30, 90C55.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"6 1","pages":"407-432"},"PeriodicalIF":2.6,"publicationDate":"2012-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82968247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-28DOI: 10.1590/S1807-03022012000200007
Liu Qingbing
In this paper, we present a new alternating local Hermitian and skew-Hermitian splitting preconditioner for solving saddle point problems. The spectral property of the preconditioned matrices is studies in detail. Theoretical results show all eigenvalues of the preconditioned matrices will generate two tight clusters, one is near (0, 0) and the other is near (2, 0) as the iteration parameter tends to zero from positive. Numerical experiments are given to validate the performances of the preconditioner. Mathematical suject classification: Primary: 65F10; Secondary: 65F50.
{"title":"An alternating LHSS preconditioner for saddle point problems","authors":"Liu Qingbing","doi":"10.1590/S1807-03022012000200007","DOIUrl":"https://doi.org/10.1590/S1807-03022012000200007","url":null,"abstract":"In this paper, we present a new alternating local Hermitian and skew-Hermitian splitting preconditioner for solving saddle point problems. The spectral property of the preconditioned matrices is studies in detail. Theoretical results show all eigenvalues of the preconditioned matrices will generate two tight clusters, one is near (0, 0) and the other is near (2, 0) as the iteration parameter tends to zero from positive. Numerical experiments are given to validate the performances of the preconditioner. Mathematical suject classification: Primary: 65F10; Secondary: 65F50.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"177 1","pages":"339-352"},"PeriodicalIF":2.6,"publicationDate":"2012-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74975205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-28DOI: 10.1590/S1807-03022012000200006
R. Farnoosh, J. Ghasemian, O. S. Fard
In this paper, we deal with the ridge-type estimator for fuzzy nonlinear regression models using fuzzy numbers and Gaussian basis functions. Shrinkage regularization methods are used in linear and nonlinear regression models to yield consistent estimators. Here, we propose a weighted ridge penalty on a fuzzy nonlinear regression model, then select the number of basis functions and smoothing parameter. In order to select tuning parameters in the regularization method, we use the Hausdorff distance for fuzzy numbers which was first suggested by Dubois and Prade [8]. The cross-validation procedure for selecting the optimal value of the smoothing parameter and the number of basis functions are fuzzified to fit the presented model. The simulation results show that our fuzzy nonlinear modelling performs well in various situations. Mathematical subject classification: Primary: 62J86; Secondary: 62J07.
{"title":"Integrating Ridge-type regularization in fuzzy nonlinear regression","authors":"R. Farnoosh, J. Ghasemian, O. S. Fard","doi":"10.1590/S1807-03022012000200006","DOIUrl":"https://doi.org/10.1590/S1807-03022012000200006","url":null,"abstract":"In this paper, we deal with the ridge-type estimator for fuzzy nonlinear regression models using fuzzy numbers and Gaussian basis functions. Shrinkage regularization methods are used in linear and nonlinear regression models to yield consistent estimators. Here, we propose a weighted ridge penalty on a fuzzy nonlinear regression model, then select the number of basis functions and smoothing parameter. In order to select tuning parameters in the regularization method, we use the Hausdorff distance for fuzzy numbers which was first suggested by Dubois and Prade [8]. The cross-validation procedure for selecting the optimal value of the smoothing parameter and the number of basis functions are fuzzified to fit the presented model. The simulation results show that our fuzzy nonlinear modelling performs well in various situations. Mathematical subject classification: Primary: 62J86; Secondary: 62J07.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"74 1","pages":"323-338"},"PeriodicalIF":2.6,"publicationDate":"2012-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85153943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-28DOI: 10.1590/S1807-03022012000200003
D. G. Yakubu, A. M. Kwami, M. Ahmed
We consider the construction of a class of numerical methods based on the general matrix inverse [14] which provides continuous interpolant for dense approximations (output). Their stability properties are similar to those for Runge-Kutta methods. These methods provide a unifying scope for many families of traditional methods. They are self-starting, to change stepsize during integration is not difficult when using them. We exploited these properties by first obtaining the direct block methods associated with the continuous schemes and then converting the block methods into uniformly A-stable high order general linear methods that are acceptable for solving stiff initial value problems. However, we will limit our formulation only for the step numbers k = 2, 3, 4. From our preliminary experiments we present some numerical results of some initial value problems in ordinary differential equations illustrating various features of the new class of methods. Mathematical subject classification: 65L05.
{"title":"A special class of continuous general linear methods","authors":"D. G. Yakubu, A. M. Kwami, M. Ahmed","doi":"10.1590/S1807-03022012000200003","DOIUrl":"https://doi.org/10.1590/S1807-03022012000200003","url":null,"abstract":"We consider the construction of a class of numerical methods based on the general matrix inverse [14] which provides continuous interpolant for dense approximations (output). Their stability properties are similar to those for Runge-Kutta methods. These methods provide a unifying scope for many families of traditional methods. They are self-starting, to change stepsize during integration is not difficult when using them. We exploited these properties by first obtaining the direct block methods associated with the continuous schemes and then converting the block methods into uniformly A-stable high order general linear methods that are acceptable for solving stiff initial value problems. However, we will limit our formulation only for the step numbers k = 2, 3, 4. From our preliminary experiments we present some numerical results of some initial value problems in ordinary differential equations illustrating various features of the new class of methods. Mathematical subject classification: 65L05.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"20 1","pages":"259-281"},"PeriodicalIF":2.6,"publicationDate":"2012-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80200415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-28DOI: 10.1590/S1807-03022012000200001
Jonu Lee, R. Sakthivel
In this paper, we implement the tanh-coth function method to construct the travelling wave solutions for (N + 1)-dimensional nonlinear evolution equations. Four models, namely the (N + 1)-dimensional generalized Boussinesq equation, (N + 1)-dimensional sine-cosine-Gordon equation, (N + 1)-double sinh-Gordon equation and (N + 1)-sinh-cosinh-Gordon equation, are used as vehicles to conduct the analysis. These equations play a very important role in mathematical physics and engineering sciences. The implemented algorithm is quite efficient and is practically well suited for these problems. The computer symbolic systems such as Maple and Mathematica allow us to perform complicated and tedious calculations. Mathematical subject classification: 35K58, 35C06, 35A25.
{"title":"Exact travelling wave solutions for some nonlinear (N+1)-dimensional evolution equations","authors":"Jonu Lee, R. Sakthivel","doi":"10.1590/S1807-03022012000200001","DOIUrl":"https://doi.org/10.1590/S1807-03022012000200001","url":null,"abstract":"In this paper, we implement the tanh-coth function method to construct the travelling wave solutions for (N + 1)-dimensional nonlinear evolution equations. Four models, namely the (N + 1)-dimensional generalized Boussinesq equation, (N + 1)-dimensional sine-cosine-Gordon equation, (N + 1)-double sinh-Gordon equation and (N + 1)-sinh-cosinh-Gordon equation, are used as vehicles to conduct the analysis. These equations play a very important role in mathematical physics and engineering sciences. The implemented algorithm is quite efficient and is practically well suited for these problems. The computer symbolic systems such as Maple and Mathematica allow us to perform complicated and tedious calculations. Mathematical subject classification: 35K58, 35C06, 35A25.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"1 1","pages":"219-243"},"PeriodicalIF":2.6,"publicationDate":"2012-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89921047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-28DOI: 10.1590/S1807-03022012000200008
M. Dehghan, M. Hajarian
An n × n real matrix P is said to be a generalized reflection matrix if PT = P and P2 = I (where PT is the transpose of P). A matrix A ∈ Rn×n is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A = P A P (A = - P A P). The reflexive and anti-reflexive matrices have wide applications in many fields. In this article, two iterative algorithms are proposed to solve the coupled matrix equations { A1 XB1 + C1XTD1 = M1. A2 XB2 + C2XTD2 = M2. over reflexive and anti-reflexive matrices, respectively. We prove that the first (second) algorithm converges to the reflexive (anti-reflexive) solution of the coupled matrix equations for any initial reflexive (anti-reflexive) matrix. Finally two numerical examples are used to illustrate the efficiency of the proposed algorithms. Mathematical subject classification: 15A06, 15A24, 65F15, 65F20.
如果PT = P且P2 = I(其中PT为P的转置)，则称n×n实矩阵P为广义反射矩阵。如果a = P a P (a = - P a P)，则称矩阵a∈Rn×n为广义反射矩阵P的自反(反)矩阵。自反矩阵和反自反矩阵在许多领域都有广泛的应用。本文提出了求解耦合矩阵方程{A1 XB1 + C1XTD1 = M1的两种迭代算法。a2xb2 + c2xtd2 = m2。分别在自反矩阵和反自反矩阵上。证明了对于任意初始自反(反)矩阵，第一(第二)算法收敛于耦合矩阵方程的自反(反)解。最后用两个数值算例说明了所提算法的有效性。数学学科分类:15A06、15A24、65F15、65F20。
{"title":"Two iterative algorithms for solving coupled matrix equations over reflexive and anti-reflexive matrices","authors":"M. Dehghan, M. Hajarian","doi":"10.1590/S1807-03022012000200008","DOIUrl":"https://doi.org/10.1590/S1807-03022012000200008","url":null,"abstract":"An n × n real matrix P is said to be a generalized reflection matrix if PT = P and P2 = I (where PT is the transpose of P). A matrix A ∈ Rn×n is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A = P A P (A = - P A P). The reflexive and anti-reflexive matrices have wide applications in many fields. In this article, two iterative algorithms are proposed to solve the coupled matrix equations { A1 XB1 + C1XTD1 = M1. A2 XB2 + C2XTD2 = M2. over reflexive and anti-reflexive matrices, respectively. We prove that the first (second) algorithm converges to the reflexive (anti-reflexive) solution of the coupled matrix equations for any initial reflexive (anti-reflexive) matrix. Finally two numerical examples are used to illustrate the efficiency of the proposed algorithms. Mathematical subject classification: 15A06, 15A24, 65F15, 65F20.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"54 1","pages":"353-371"},"PeriodicalIF":2.6,"publicationDate":"2012-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78339265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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