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The Conditions for the Convergence of Power Scaled Matrices and Applications 幂标度矩阵收敛的条件及其应用
Am. J. Comput. Math. Pub Date : 2011-06-30 DOI: 10.4236/ajcm.2011.12007
Xuzhou Chen, R. Hartwig
{"title":"The Conditions for the Convergence of Power Scaled Matrices and Applications","authors":"Xuzhou Chen, R. Hartwig","doi":"10.4236/ajcm.2011.12007","DOIUrl":"https://doi.org/10.4236/ajcm.2011.12007","url":null,"abstract":"For an invertible diagonal matrix D , the convergence of the power scaled matrix sequence N N D A  is investigated. As a special case, necessary and sufficient conditions are given for the convergence of NN D T  , where T is triangular. These conditions involve both the spectrum as well as the diagraph of the matrix T . The results are then used to privide a new proof for the convergence of subspace iteration.","PeriodicalId":359476,"journal":{"name":"Am. J. Comput. Math.","volume":"961 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127033701","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
Strong-Stability-Preserving, K-Step, 5- to 10-Stage, Hermite-Birkhoff Time-Discretizations of Order 12 强稳定保持，k阶，5 ~ 10阶，12阶Hermite-Birkhoff时间离散
Am. J. Comput. Math. Pub Date : 2011-06-30 DOI: 10.4236/ajcm.2011.12008
T. Nguyen-Ba, H. Nguyen-Thu, R. Vaillancourt
{"title":"Strong-Stability-Preserving, K-Step, 5- to 10-Stage, Hermite-Birkhoff Time-Discretizations of Order 12","authors":"T. Nguyen-Ba, H. Nguyen-Thu, R. Vaillancourt","doi":"10.4236/ajcm.2011.12008","DOIUrl":"https://doi.org/10.4236/ajcm.2011.12008","url":null,"abstract":"We construct optimal k-step, 5- to 10-stage, explicit, strong-stability-preserving Hermite-Birkhoff (SSP HB) methods of order 12 with nonnegative coefficients by combining linear k-step methods of order 9 with 5- to 10-stage Runge-Kutta (RK) methods of order 4. Since these methods maintain the monotonicity property, they are well suited for solving hyperbolic PDEs by the method of lines after a spatial discretization. It is seen that the 8-step 7-stage HB methods have largest effective SSP coefficient among the HB methods of order 12 on hand. On Burgers’ equations, some of the new HB methods have larger maximum effective CFL numbers than Huang’s 7-step hybrid method of order 7, thus allowing larger step size.","PeriodicalId":359476,"journal":{"name":"Am. J. Comput. Math.","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114112990","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 Multi-Step Differential Transform Method on Flow of a Second-Grade Fluid over a Stretching or Shrinking Sheet 多步微分变换法在二级流体在拉伸或收缩薄片上流动中的应用
Am. J. Comput. Math. Pub Date : 2011-06-30 DOI: 10.4236/ajcm.2011.12012
Mohammad Mehdi Rashidi, Ali J. Chamkha, M. Keimanesh
{"title":"Application of Multi-Step Differential Transform Method on Flow of a Second-Grade Fluid over a Stretching or Shrinking Sheet","authors":"Mohammad Mehdi Rashidi, Ali J. Chamkha, M. Keimanesh","doi":"10.4236/ajcm.2011.12012","DOIUrl":"https://doi.org/10.4236/ajcm.2011.12012","url":null,"abstract":"In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solutions are only valid for small values of the independent variable. The DTM solutions diverge for some differential equations that extremely have nonlinear behaviors or have boundary-conditions at infinity. For this reason the governing boundary-layer equations are solved by the Multi-step Differential Transform Method (MDTM). The main advantage of this method is that it can be applied directly to nonlinear differential equations without requiring linearization, discretization, or perturbation. It is a semi analytical-numerical technique that formulizes Taylor series in a very different manner. By applying the MDTM the interval of convergence for the series solution is increased. The MDTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. It is predicted that the MDTM can be applied to a wide range of engineering applications.","PeriodicalId":359476,"journal":{"name":"Am. J. Comput. Math.","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126491111","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: 68
Characteristic Analysis of Exponential Compact Higher Order Schemes for Convection-Diffusion Equations 对流扩散方程指数紧高阶格式的特征分析
Am. J. Comput. Math. Pub Date : 2011-06-30 DOI: 10.4236/ajcm.2011.12005
Y. Sanyasiraju, Nachiketa Mishra
{"title":"Characteristic Analysis of Exponential Compact Higher Order Schemes for Convection-Diffusion Equations","authors":"Y. Sanyasiraju, Nachiketa Mishra","doi":"10.4236/ajcm.2011.12005","DOIUrl":"https://doi.org/10.4236/ajcm.2011.12005","url":null,"abstract":"This paper looks at the development of a class of Exponential Compact Higher Order (ECHO) schemes and attempts to comprehend their behaviour by introducing different combinations of discrete source function and its derivatives. The characteristic analysis is performed for one-dimensional schemes to understand the efficiency of the scheme and a similar analysis has been introduced for higher dimensional schemes. Finally, the developed schemes are used to solve several example problems and compared the error norms and rates of convergence.","PeriodicalId":359476,"journal":{"name":"Am. J. Comput. Math.","volume":"483 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115872575","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
Magneto Hydrodynamic Orthogonal Stagnation Point Flow of a Power-Law Fluid Toward a Stretching Surface 幂律流体向拉伸表面的磁流体力学正交滞止点流动
Am. J. Comput. Math. Pub Date : 2011-06-30 DOI: 10.4236/ajcm.2011.12013
Manisha Patel, M. G. Timol
{"title":"Magneto Hydrodynamic Orthogonal Stagnation Point Flow of a Power-Law Fluid Toward a Stretching Surface","authors":"Manisha Patel, M. G. Timol","doi":"10.4236/ajcm.2011.12013","DOIUrl":"https://doi.org/10.4236/ajcm.2011.12013","url":null,"abstract":"Steady two dimensional MHD stagnation point flow of a power law fluid over a stretching surface is investigated when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation point. The fluid impinges on the surface is considered orthogonally. Numerical and analytical solutions are obtained for different cases.","PeriodicalId":359476,"journal":{"name":"Am. J. Comput. Math.","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125778628","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: 13
An Exponential Series Method for the Solution of Free Convection Boundary Layer Flow in a Saturated Porous Medium 饱和多孔介质自由对流边界层流动的指数级数解法
Am. J. Comput. Math. Pub Date : 2011-06-30 DOI: 10.4236/ajcm.2011.12010
V. Awati, N. M. Bujurke, R. B. Kudenatti
{"title":"An Exponential Series Method for the Solution of Free Convection Boundary Layer Flow in a Saturated Porous Medium","authors":"V. Awati, N. M. Bujurke, R. B. Kudenatti","doi":"10.4236/ajcm.2011.12010","DOIUrl":"https://doi.org/10.4236/ajcm.2011.12010","url":null,"abstract":"Third order nonlinear ordinary differential equation, subject to appropriate boundary conditions, arising in fluid mechanics is solved exactly using more suggestive schemes- Dirichlet series and method of stretching variables. These methods have advantages over pure numerical methods in obtaining derived quantities accurately for various values of the parameters involved at a stretch and are valid in a much larger domain compared with classical numerical schemes.","PeriodicalId":359476,"journal":{"name":"Am. J. Comput. Math.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129161190","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: 7
The Odd-Point Ternary Approximating Schemes 奇点三元逼近格式
Am. J. Comput. Math. Pub Date : 2011-06-30 DOI: 10.4236/ajcm.2011.12011
G. Mustafa, A. Ghaffar, F. Khan
{"title":"The Odd-Point Ternary Approximating Schemes","authors":"G. Mustafa, A. Ghaffar, F. Khan","doi":"10.4236/ajcm.2011.12011","DOIUrl":"https://doi.org/10.4236/ajcm.2011.12011","url":null,"abstract":"We present a general formula to generate the family of odd-point ternary approximating subdivision schemes with a shape parameter for describing curves. The influence of parameter to the limit curves and the sufficient conditions of the continuities from C0 to C5 of 3- and 5-point schemes are discussed. Our family of 3-point and 5-point ternary schemes has higher order of derivative continuity than the family of 3-point and 5-point schemes presented by [Jian-ao Lian, On a-ary subdivision for curve design: II. 3-point and 5-point interpolatory schemes, Applications and Applied Mathematics: An International Journal, 3(2), 2008, 176-187]. Moreover, a 3-point ternary cubic B-spline is special case of our family of 3-point ternary scheme. The visual quality of schemes with examples is also demonstrated.","PeriodicalId":359476,"journal":{"name":"Am. J. Comput. Math.","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121214895","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: 23
Thermal and Mechanical Modeling of Fluid and Heat Flow in a Porous Metal Using Neural Networks for Application as TPS in Space Vehicles 基于神经网络的多孔金属流体和热流热力学建模及其在航天飞行器TPS中的应用
Am. J. Comput. Math. Pub Date : 2011-06-30 DOI: 10.4236/ajcm.2011.12015
M. PrabhuS.
{"title":"Thermal and Mechanical Modeling of Fluid and Heat Flow in a Porous Metal Using Neural Networks for Application as TPS in Space Vehicles","authors":"M. PrabhuS.","doi":"10.4236/ajcm.2011.12015","DOIUrl":"https://doi.org/10.4236/ajcm.2011.12015","url":null,"abstract":"This paper contains novel model using feedback neural networks for a work piece temperature predic- tion.The heat and mass transfer in a porous metal workpiece which is heated by a fire gun is studied. The heat flux distribution is determined by thermocouple connected on the workpiece at definite distances. The gun work piece distance were also change and the temperature distribution and heat flux were determined. The permeability’s were in range of 0.01 – 0.15 .The ANN model parameters of the result output were simu- lated using the ANN parameters The simulation was done using MATLAB 6.0® Neural Network Toolbox.","PeriodicalId":359476,"journal":{"name":"Am. J. Comput. Math.","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129918222","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
Numerical Solution of Obstacle Problems by B-Spline Functions 用b样条函数数值解障碍问题
Am. J. Comput. Math. Pub Date : 2011-06-30 DOI: 10.4236/ajcm.2011.12006
G. B. Loghmani, F. Mahdifar, S. R. Alavizadeh
{"title":"Numerical Solution of Obstacle Problems by B-Spline Functions","authors":"G. B. Loghmani, F. Mahdifar, S. R. Alavizadeh","doi":"10.4236/ajcm.2011.12006","DOIUrl":"https://doi.org/10.4236/ajcm.2011.12006","url":null,"abstract":"In this study, we use B-spline functions to solve the linear and nonlinear special systems of differential equations associated with the category of obstacle, unilateral, and contact problems. The problem can easily convert to an optimal control problem. Then a convergent approximate solution is constructed such that the exact boundary conditions are satisfied. The numerical examples and computational results illustrate and guarantee a higher accuracy for this technique.","PeriodicalId":359476,"journal":{"name":"Am. J. Comput. Math.","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133593705","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
Conjugate Effects of Radiation and Joule Heating on Magnetohydrodynamic Free Convection Flow along a Sphere with Heat Generation 辐射和焦耳加热对产生热量的球体磁流体动力自由对流的共轭效应
Am. J. Comput. Math. Pub Date : 2011-03-30 DOI: 10.4236/ajcm.2011.11003
M. Ali, M. A. Alim, L. S. Andallah
{"title":"Conjugate Effects of Radiation and Joule Heating on Magnetohydrodynamic Free Convection Flow along a Sphere with Heat Generation","authors":"M. Ali, M. A. Alim, L. S. Andallah","doi":"10.4236/ajcm.2011.11003","DOIUrl":"https://doi.org/10.4236/ajcm.2011.11003","url":null,"abstract":"The conjugate effects of radiation and joule heating on magnetohydrodynamic (MHD) free convection flow along a sphere with heat generation have been investigated in this paper. The governing equations are transformed into dimensionless non-similar equations by using set of suitable transformations and solved numerically by the finite difference method along with Newton’s linearization approximation. Attention has been focused on the evaluation of shear stress in terms of local skin friction and rate of heat transfer in terms of local Nusselt number, velocity as well as temperature profiles. Numerical results have been shown graphically for some selected values of parameters set consisting of heat generation parameter Q, radiation parameter Rd, magnetic parameter M, joule heating parameter J and the Prandtl number Pr.","PeriodicalId":359476,"journal":{"name":"Am. J. Comput. Math.","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115342759","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: 8
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