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Nonlinear Algebraic Equations Solved by an Optimal Splitting-Linearizing Iterative Method
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作者 Chein-Shan Liu Essam REl-Zahar Yung-Wei Chen 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第5期1111-1130,共20页
How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linea... How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linearizing technique based on the nonlinear term to reduce the effect of the nonlinear terms.We decompose the nonlinear terms in the NAEs through a splitting parameter and then linearize the NAEs around the values at the previous step to a linear system.Through the maximal orthogonal projection concept,to minimize a merit function within a selected interval of splitting parameters,the optimal parameters can be quickly determined.In each step,a linear system is solved by the Gaussian elimination method,and the whole iteration procedure is convergent very fast.Several numerical tests show the high performance of the optimal split-linearization iterative method(OSLIM). 展开更多
关键词 Nonlinear algebraic equations novel splitting-linearizing technique iterative method maximal projection optimal splitting parameter
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A NEW ALGORITHM FOR SOLVING DIFFERENTIAL/ALGEBRAIC EQUATIONS OF MULTIBODY SYSTEM DYNAMICS
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作者 王艺兵 赵维加 潘振宽 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1997年第9期905-912,共8页
The second order Euler-Lagrange equations are transformed to a set of first order differential/algebraic equations, which are then transformed to state equations by using local parameterization. The corresponding disc... The second order Euler-Lagrange equations are transformed to a set of first order differential/algebraic equations, which are then transformed to state equations by using local parameterization. The corresponding discretization method is presented, and the results can be used to implementation of various numerical integration methods. A numerical example is presented finally. 展开更多
关键词 multibody systems differential/algebraic equations numerical analysis
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THE SOLUTION FOR THE GENERALIZED RICCATIALGEBRAIC EQUATIONS OF LINEAR EQUALITY CONSTRAINT SYSTEM
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作者 邓子辰 钟万勰 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1998年第4期309-313,共5页
Based on the dynamic equation, the performance functional and the system constraint equation of time-invariant discrete LQ control problem, the generalized Riccati equations of linear equality constraint system are ob... Based on the dynamic equation, the performance functional and the system constraint equation of time-invariant discrete LQ control problem, the generalized Riccati equations of linear equality constraint system are obtained according to the minimum principle, then a deep discussion about the above equations is given, and finally numerical example is shown in this paper. 展开更多
关键词 constraint equation generalized Riccati algebraic equation linear quadratic control
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On the growth of transcendental entire solutions of algebraic differential equations 被引量:2
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作者 朱玲妹 杨德贵 王小灵 《Journal of Southeast University(English Edition)》 EI CAS 2003年第1期98-102,共5页
In this paper, we investigate the growth of transcendental entire solutionsof the following algebraic differential equation a(z)f'~2 +(b_2(z)f^2 +b_1(z)f +b_0(z))f'=d_3(z)f^3+d_2(z)f^2 +d_1(z)f +d_0(z), where ... In this paper, we investigate the growth of transcendental entire solutionsof the following algebraic differential equation a(z)f'~2 +(b_2(z)f^2 +b_1(z)f +b_0(z))f'=d_3(z)f^3+d_2(z)f^2 +d_1(z)f +d_0(z), where a(z), b_i(z) (0<- i <=2) and d_j (z) (0<=j<= 3) are allpolynomials, and this equation relates closely to the following well-known algebraic differentialequation C(z,w)w'~2 + B(z,w)w' + A(z,w) =0, where G(z,w)not ident to 0, B(z,w) and A(z,w) are threepolynomials in z and w. We give relationships between the growth of entire solutions and the degreesof the above three polynomials in detail. 展开更多
关键词 algebraic differential equation DEGREE entire solutions
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Application of HAM for Nonlinear Integro-Differential Equations of Order Two
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作者 Zainidin Eshkuvatov Davron Khayrullaev +2 位作者 Muzaffar Nurillaev Shalela Mohd Mahali Anvar Narzullaev 《Journal of Applied Mathematics and Physics》 2023年第1期55-68,共14页
In this work, we consider the second order nonlinear integro-differential Equation (IDEs) of the Volterra-Fredholm type. One of the popular methods for solving Volterra or Fredholm type IDEs is the method of quadratur... In this work, we consider the second order nonlinear integro-differential Equation (IDEs) of the Volterra-Fredholm type. One of the popular methods for solving Volterra or Fredholm type IDEs is the method of quadrature while the problem of consideration is a linear problem. If IDEs are nonlinear or integral kernel is complicated, then quadrature rule is not most suitable;therefore, other types of methods are needed to develop. One of the suitable and effective method is homotopy analysis method (HAM) developed by Liao in 1992. To apply HAM, we firstly reduced the IDEs into nonlinear integral Equation (IEs) of Volterra-Fredholm type;then the standard HAM was applied. Gauss-Legendre quadrature formula was used for kernel integrations. Obtained system of algebraic equations was solved numerically. Moreover, numerical examples demonstrate the high accuracy of the proposed method. Comparisons with other methods are also provided. The results show that the proposed method is simple, effective and dominated other methods. 展开更多
关键词 Integral-Differential equations Homotopy Analyses Method Iterative System algebraic equations Gauss-Legendre Quadrature Formula
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THE GROWTH OF SOLUTIONS OF SYSTEMS OF COMPLEX NONLINEAR ALGEBRAIC DIFFERENTIAL EQUATIONS 被引量:19
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作者 高凌云 《Acta Mathematica Scientia》 SCIE CSCD 2010年第3期932-938,共7页
We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations... We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations. 展开更多
关键词 Growth order algebraic differential equations entire function
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ON THE GROWTH OF SOLUTIONS OF HIGHER-ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS 被引量:6
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作者 高凌云 《Acta Mathematica Scientia》 SCIE CSCD 2002年第4期459-465,共7页
Using Nevanlinna theory of the value distribution of meromorphic functions, the author investigates the problem of the growth of solutions of two types of algebraic differential equation and obtains some results.
关键词 the growth algebraic differential equations algebroid solutions
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Generalized Higher-Order Algebraic Differential Equations with Admissible Algebroid Solutions 被引量:4
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作者 高凌云 《Northeastern Mathematical Journal》 CSCD 2001年第2期159-168,共10页
Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
关键词 algebroid functions admissible solution generalized higher order algebraic differential equations.
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On the Order of the Solutions of Systems of Complex Algebraic Differential Equations 被引量:1
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作者 SU Xian-feng GAO Ling-yun 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第2期196-199,共4页
This paper is concerned with the order of the solutions of systems of high-order complex algebraic differential equations.By means of Zalcman Lemma,the systems of equations of[1]is extended to more general form.
关键词 normal family order systems of complex algebraic differential equations
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ON HYPER-ORDER OF MEROMORPHIC SOLUTIONS OF FIRST-ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS
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作者 李叶舟 冯绍继 《Acta Mathematica Scientia》 SCIE CSCD 2001年第3期383-390,共8页
The authors give a precise estimate of the hyper-order of meromorphic solutions of general first-order algebraic differential equations.
关键词 algebraic differential equation meromorphic solution HYPER-ORDER ZERO POLE
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GROWTH OF MEROMORPHIC SOLUTIONS OF SOME ALGEBRAIC DIFFERENTIAL EQUATIONS
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作者 李叶舟 戚建明 袁文俊 《Acta Mathematica Scientia》 SCIE CSCD 2015年第1期105-111,共7页
In this paper, by means of the normal family theory, we estimate the growth order of meromorphic solutions of some algebraic differential equations and improve the related result of Barsegian et al. [6]. We also give ... In this paper, by means of the normal family theory, we estimate the growth order of meromorphic solutions of some algebraic differential equations and improve the related result of Barsegian et al. [6]. We also give some examples to show that our results occur in some special cases. 展开更多
关键词 the normal family theory algebraic differential equations meromorphic solutions GROWTH
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A NOTE ON MALMQUIST-YOSIDA TYPE THEOREM OF HIGHER ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS
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作者 张建军 廖良文 《Acta Mathematica Scientia》 SCIE CSCD 2018年第2期471-478,共8页
In this article, we give a simple proof of Malmquist-Yosida type theorem of higher order algebraic differential equations, which is different from the methods as that of Gackstatter and Laine [2], and Steinmetz [12].
关键词 Malmquist-Yosida type theorem algebraic differential equations meromorphicsolutions
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On Results the Growth of Meromorphic Solutions of Algebraic Diferential Equations
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作者 Su Xian-feng Li Xiao-meng +1 位作者 He Zhong-wei Ji You-qing 《Communications in Mathematical Research》 CSCD 2013年第4期345-350,共6页
In this paper, we give an estimate result of Gol'dberg's theorem concern- ing the growth of meromorphic solutions of Mgebraic differential equations by using Zalcman Lemma. It is an extending result of the correspon... In this paper, we give an estimate result of Gol'dberg's theorem concern- ing the growth of meromorphic solutions of Mgebraic differential equations by using Zalcman Lemma. It is an extending result of the corresponding theorem by Yuan et al. (Yuan W J, Xiao B, Zhang J J. The general theorem of Gol'dberg concerning the growth of meromorphic solutions of algebraic differential equations. Comput. Math. Appl., 2009, 58:1788 1791). Meanwhile, we also take some examples to show that our estimate is sharp. 展开更多
关键词 meromorphic function algebraic differential equation normal family spherical derivative
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On the Counting Functions of Meromorphic Solutions of Systems of Higher-order Algebraic Differential Equations
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作者 CHEN Miao-ling GAO Ling-yun 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第1期7-10,共4页
Using Nevanlinna theory and value distribution of meromorphic functions and the other techniques,we investigate the counting functions of meromorphic solutions of systems of higher-order algebraic differential equatio... Using Nevanlinna theory and value distribution of meromorphic functions and the other techniques,we investigate the counting functions of meromorphic solutions of systems of higher-order algebraic differential equations and obtain some results. 展开更多
关键词 meromorphic solution algebraic differential equations counting function
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Numerical Solution of Constrained Mechanical System Motions Equations and Inverse Problems of Dynamics 被引量:2
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作者 R.G. Muharliamov (Russian Peoples’ Friendship University, 117198, Moscow, Mikluho Maklaya,6,Russia.) 《应用数学》 CSCD 北大核心 2001年第2期103-119,共17页
In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarant... In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined. 展开更多
关键词 Kinematies Dynamical equations CONSTRAINTS Lagrange’s equations Rigid body Numerical solution Differential algebraic equations
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On the First-degree Algebraic Equation of the Generalized Quaternion
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作者 蔡永裕 《Chinese Quarterly Journal of Mathematics》 CSCD 2002年第2期59-64,共6页
In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained ... In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained critical conditions on existence of a unique solution, infinitely many solutions or nonexistence any solution for the two classes algebraic equation. 展开更多
关键词 generalized quaternion first_degree algebraic equation matrix representation
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Solution of Algebraic Lyapunov Equation on Positive-Definite Hermitian Matrices by Using Extended Hamiltonian Algorithm 被引量:1
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作者 Muhammad Shoaib Arif Mairaj Bibi Adnan Jhangir 《Computers, Materials & Continua》 SCIE EI 2018年第2期181-195,共15页
This communique is opted to study the approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices.We choose the geodesic distance between􀀀AHX􀀀XA an... This communique is opted to study the approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices.We choose the geodesic distance between􀀀AHX􀀀XA and P as the cost function,and put forward the Extended Hamiltonian algorithm(EHA)and Natural gradient algorithm(NGA)for the solution.Finally,several numerical experiments give you an idea about the effectiveness of the proposed algorithms.We also show the comparison between these two algorithms EHA and NGA.Obtained results are provided and analyzed graphically.We also conclude that the extended Hamiltonian algorithm has better convergence speed than the natural gradient algorithm,whereas the trajectory of the solution matrix is optimal in case of Natural gradient algorithm(NGA)as compared to Extended Hamiltonian Algorithm(EHA).The aim of this paper is to show that the Extended Hamiltonian algorithm(EHA)has superior convergence properties as compared to Natural gradient algorithm(NGA).Upto the best of author’s knowledge,no approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices is found so far in the literature. 展开更多
关键词 Information geometry algebraic lyapunov equation positive-definite hermitianmatrix manifold natural gradient algorithm extended hamiltonian algorithm
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ALGEBRAIC DIFFERENTIAL INDEPENDENCE CONCERNING THE EULER Γ-FUNCTION AND DIRICHLET SERIES
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作者 Wei CHEN Qiong WANG 《Acta Mathematica Scientia》 SCIE CSCD 2020年第4期1035-1044,共10页
This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class F which contains Dirichlet L-functions,L-functions in the extended Selberg class... This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class F which contains Dirichlet L-functions,L-functions in the extended Selberg class, or some periodic functions. We prove that the EulerΓ-function and the function F cannot satisfy any nontrivial algebraic differential equations whose coefficients are meromorphic functions Ø with ρ(Ø) < 1. 展开更多
关键词 Gamma function L-FUNCTIONS algebraic differential independence algebraic differential equations
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Global Existence of Positive Solutions for Volterra Integral Equations
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作者 王术 万春林 张锟 《Chinese Quarterly Journal of Mathematics》 CSCD 1995年第3期97-101,共5页
This paper considers the global existence and nonexistence of positive solutions for the following volterra integral equations wbers Matrix B is called a positive definite one, if all the principal minors have positi... This paper considers the global existence and nonexistence of positive solutions for the following volterra integral equations wbers Matrix B is called a positive definite one, if all the principal minors have positive detechants. By considering the existence of positivve solutions for algebra equations, it is proved that if I-A is a positive definite matrix,where I is an identity matrix, then (I) bas global positive solution 1 Otherwise, (I)has no continous nbndeereasing positive solution. 展开更多
关键词 volterra inegral equations global solution positive solution of algebra equations
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A Maple Package on Symbolic Computation of Hirota Bilinear Form for Nonlinear Equations
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作者 YANG Xu-Dong RUAN Hang-Yu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第11期801-807,共7页
An improved algorithm for symbolic computation of Hirota bilinear forms of KdV-type equations withlogarithmic transformations is presented.In the algorithm,the general assumption of Hirota bilinear form is successfull... An improved algorithm for symbolic computation of Hirota bilinear forms of KdV-type equations withlogarithmic transformations is presented.In the algorithm,the general assumption of Hirota bilinear form is successfullyreduced based on the property of uniformity in rank.Furthermore,we discard the integral operation in the traditionalalgorithm.The software package HBFTrans is written in Maple and its running effectiveness is tested by a variety solitonequations. 展开更多
关键词 Hirota bilinear form nonlinear equation symbolic algebra
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