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An Extended Numerical Method by Stancu Polynomials for Solution of Integro-Differential Equations Arising in Oscillating Magnetic Fields
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作者 Neşe İşler Acar 《Advances in Pure Mathematics》 2024年第10期785-796,共12页
In this study, the Bernstein collocation method has been expanded to Stancu collocation method for numerical solution of the charged particle motion for certain configurations of oscillating magnetic fields modelled b... In this study, the Bernstein collocation method has been expanded to Stancu collocation method for numerical solution of the charged particle motion for certain configurations of oscillating magnetic fields modelled by a class of linear integro-differential equations. As the method has been improved, the Stancu polynomials that are generalization of the Bernstein polynomials have been used. The method has been tested on a physical problem how the method can be applied. Moreover, numerical results of the method have been compared with the numerical results of the other methods to indicate the efficiency of the method. 展开更多
关键词 Stancu Polynomials Collocation Method Integro-differential equations linear equation Systems Matrix equations
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Equation governing the probability density evolution of multi-dimensional linear fractional differential systems subject to Gaussian white noise
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作者 Yi Luo Meng-Ze Lyu +1 位作者 Jian-Bing Chen Pol D.Spanos 《Theoretical & Applied Mechanics Letters》 CAS CSCD 2023年第3期199-208,共10页
Stochastic fractional differential systems are important and useful in the mathematics,physics,and engineering fields.However,the determination of their probabilistic responses is difficult due to their non-Markovian ... Stochastic fractional differential systems are important and useful in the mathematics,physics,and engineering fields.However,the determination of their probabilistic responses is difficult due to their non-Markovian property.The recently developed globally-evolving-based generalized density evolution equation(GE-GDEE),which is a unified partial differential equation(PDE)governing the transient probability density function(PDF)of a generic path-continuous process,including non-Markovian ones,provides a feasible tool to solve this problem.In the paper,the GE-GDEE for multi-dimensional linear fractional differential systems subject to Gaussian white noise is established.In particular,it is proved that in the GE-GDEE corresponding to the state-quantities of interest,the intrinsic drift coefficient is a time-varying linear function,and can be analytically determined.In this sense,an alternative low-dimensional equivalent linear integer-order differential system with exact closed-form coefficients for the original highdimensional linear fractional differential system can be constructed such that their transient PDFs are identical.Specifically,for a multi-dimensional linear fractional differential system,if only one or two quantities are of interest,GE-GDEE is only in one or two dimensions,and the surrogate system would be a one-or two-dimensional linear integer-order system.Several examples are studied to assess the merit of the proposed method.Though presently the closed-form intrinsic drift coefficient is only available for linear stochastic fractional differential systems,the findings in the present paper provide a remarkable demonstration on the existence and eligibility of GE-GDEE for the case that the original high-dimensional system itself is non-Markovian,and provide insights for the physical-mechanism-informed determination of intrinsic drift and diffusion coefficients of GE-GDEE of more generic complex nonlinear systems. 展开更多
关键词 Globally-evolving-based generalized density evolution equation(GE-GDEE) linear fractional differential system Non-Markovian system Analytical intrinsic drift coefficient Dimension reduction
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The Existence of Meromorphic Solutions to Non-Linear Delay Differential Equations
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作者 Mingyue Wu 《Open Journal of Applied Sciences》 2023年第12期2329-2342,共14页
In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational c... In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational coefficients, k is a positive integer. Under the assumption when above equations own transcendental meromorphic solutions with minimal hyper-type, we derive the concrete conditions on the degree of the right side of them. Specially, when w(z)=0 is a root of , its multiplicity is at most k. Some examples are given here to illustrate that our results are accurate. 展开更多
关键词 Non-linear Delay differential equations Painlevé Type equations Nevanlinna Theory Meromorphic Function Solutions Minimal Hypertype
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Higher-order differential variational principle and differential equations of motion for mechanical systems in event space
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作者 张相武 李院院 +1 位作者 赵小侠 罗文峰 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第10期292-298,共7页
In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d'Alembert principle of the system, the... In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d'Alembert principle of the system, the higher-order velocity energy and the higher-order acceleration energy of the system in event space are defined, the higher-order d'Alembert- Lagrange principle of the system in event space is established, and the parametric forms of Euler-Lagrange, Nielsen and Appell for this principle are given. Finally, the higher-order differential equations of motion for holonomic systems in event space are obtained. 展开更多
关键词 event space the higher-order d'Alembert-Lagrange principle the higher-order time rate of changeof force the higher-order differential equations of motion
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THE STABILITY OF LINEAR MULTISTEP METHODS FOR SYSTEMS OF DELAY DIFFERENTIAL EQUATIONS 被引量:2
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作者 田红炯 匡蛟勋 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 1995年第1期10-16,共7页
This paper deals with the numerical solution of initial value problems for systems of differential equations with a delay argument. The numerical stability of a linear multistep method is investigated by analysing the... This paper deals with the numerical solution of initial value problems for systems of differential equations with a delay argument. The numerical stability of a linear multistep method is investigated by analysing the solution of the lest equation y’(t)=Ay(t) + By(1-t),where A,B denote constant complex N×N-matrices,and t】0.We investigate carefully the characterization of the stability region. 展开更多
关键词 NUMERICAL stability linear mullistep method DELAY differential equation.
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ESTIMATES FOR THE HYPER-ORDER OF SOLUTIONS OF CERTAIN LINEAR DIFFERENTIAL EQUATIONS 被引量:2
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作者 江良英 陈宗煊 《Acta Mathematica Scientia》 SCIE CSCD 2008年第2期393-400,共8页
In this article, the authors study the growth of certain second order linear differential equation f″+A(z)f′+B(z)f=0 and give precise estimates for the hyperorder of solutions of infinite order. Under similar ... In this article, the authors study the growth of certain second order linear differential equation f″+A(z)f′+B(z)f=0 and give precise estimates for the hyperorder of solutions of infinite order. Under similar conditions, higher order differential equations will be considered. 展开更多
关键词 linear differential equation entire function HYPER-ORDER GENUS
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Roughness of Exponential Estimates for Linear Functional Differential Equations 被引量:9
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作者 Wang Zhen (Anhui University) 《大学数学》 1994年第S1期146-150,共5页
Assume that the fundamental solution matrix U (t, s ) of x’(t)=L(t, x,) satisfies |U(t,s)|≤Ke-e(t-s) for t≥s.If|(t,φ)|≤δ|φ(0)|with δ【a/K, then the fundamental solution matrix of the perturbed equation x’(t)=... Assume that the fundamental solution matrix U (t, s ) of x’(t)=L(t, x,) satisfies |U(t,s)|≤Ke-e(t-s) for t≥s.If|(t,φ)|≤δ|φ(0)|with δ【a/K, then the fundamental solution matrix of the perturbed equation x’(t)=L(t,x,)+(t ,x,) also possesses similar exponential estimate. For α=0, a similar result is given. 展开更多
关键词 linear functional differential equation FUNDAMENTAL solution matrix
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On the Growth of Solutions of a Class of Higher Order Linear Differential Equations with Meromorphic Coefficients 被引量:2
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作者 MAO Zhi-qiang LIU Hui-fang 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第2期278-283,共6页
In this paper, we investigate the growth of solutions of higher order linear differential equations with meromorphic coefficients. Under certain conditions, we obtain precise estimation of growth order and hyper-order... In this paper, we investigate the growth of solutions of higher order linear differential equations with meromorphic coefficients. Under certain conditions, we obtain precise estimation of growth order and hyper-order of solutions of the equation. 展开更多
关键词 linear differential equation meromorphic function growth order HYPER-ORDER
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ON GLOBAL MEROMORPHIC SOLUTIONS OF SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS 被引量:1
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作者 孔荫莹 孙道椿 《Acta Mathematica Scientia》 SCIE CSCD 2013年第2期423-429,共7页
The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory ... The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory of such equations. 展开更多
关键词 Second-order linear differential equations global meromorphic solutions mero-morphic continuation
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DIFFERENTIATOR SERIES SOLUTION OF LINEAR DIFFERENTIAL ORDINARY EQUATION
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作者 柯红路 谢和熙 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第8期59-66,共8页
In this paper, the principle techinique of the differentiator method, and some examples using the method to obtain the general solution and special solution of the differential equation are introduced. The essential d... In this paper, the principle techinique of the differentiator method, and some examples using the method to obtain the general solution and special solution of the differential equation are introduced. The essential difference between this method and the others is that by this method special and general solutions can be obtained directly with the operations of the differentor in the differential equation and without the enlightenment of other scientific knowledge. 展开更多
关键词 linear ordinary differential equation differentiator series method special solution general solution
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EXISTENCE OF MEROMORPHIC SOLUTIONS OF SOME HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS
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作者 张晓梅 孙道椿 《Acta Mathematica Scientia》 SCIE CSCD 2013年第2期600-608,共9页
This article discusses the problems on the existence of meromorphic solutions of some higher order linear differential equations with meromorphic coefficients. Some nice results are obtained. And these results perfect... This article discusses the problems on the existence of meromorphic solutions of some higher order linear differential equations with meromorphic coefficients. Some nice results are obtained. And these results perfect the complex oscillation theory of meromorphic solutions of linear differential equations. 展开更多
关键词 Higher order linear differential equation meromorphic coefficient meromorphicsolutions the first coefficient
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INSTABILITY OF SOLUTION FOR THE FOURTH ORDER LINEAR DIFFERENTIAL EQUATION WITH VARIED COEFFICIENT
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作者 卢德渊 廖宗璜 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1993年第5期481-497,共17页
In this paper, we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part,... In this paper, we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part, by means of Liapunov's second method. 展开更多
关键词 ordinary differential equation motive stability theory linear differential equation with varied coefficient
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Criteria for System of Three Second-Order Ordinary Differential Equations to Be Reduced to a Linear System via Restricted Class of Point Transformation
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作者 Supaporn Suksern Nawee Sakdadech 《Applied Mathematics》 2014年第3期553-571,共19页
This paper is devoted to the study of the linearization problem of system of three second-order ordinary differential equations and . The necessary conditions for linearization by general point transformation and are ... This paper is devoted to the study of the linearization problem of system of three second-order ordinary differential equations and . The necessary conditions for linearization by general point transformation and are found. The sufficient conditions for linearization by restricted class of point transformation and are obtained. Moreover, the procedure for obtaining the linearizing transformation is provided in explicit forms. Examples demonstrating the procedure of using the linearization theorems are presented. 展开更多
关键词 linearIZATION Problem Point Transformation SYSTEM of THREE SECOND-ORDER Ordinary differential equation
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Stability of linear multistep methods for delay differential equations in the light of Kreiss resolvent condition
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作者 赵景军 刘明珠 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2001年第2期155-158,共4页
This paper deals with the stability analysis of the linear multistep (LM) methods in the numerical solution of delay differential equations. Here we provide a qualitative stability estimates, pertiment to the classica... This paper deals with the stability analysis of the linear multistep (LM) methods in the numerical solution of delay differential equations. Here we provide a qualitative stability estimates, pertiment to the classical scalar test problem of the form y′(t)=λy(t)+μy(t-τ) with τ>0 and λ,μ are complex, by using (vartiant to) the resolvent condition of Kreiss. We prove that for A stable LM methods the upper bound for the norm of the n th power of square matrix grows linearly with the order of the matrix. 展开更多
关键词 Delay differential equations linear multistep methods resolvent condition
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Double Elzaki Transform Decomposition Method for Solving Non-Linear Partial Differential Equations 被引量:1
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作者 Moh A. Hassan Tarig M. Elzaki 《Journal of Applied Mathematics and Physics》 2020年第8期1463-1471,共9页
In this paper, we discuss a new method employed to tackle non-linear partial differential equations, namely Double Elzaki Transform Decomposition Method (DETDM). This method is a combination of the Double ELzaki Trans... In this paper, we discuss a new method employed to tackle non-linear partial differential equations, namely Double Elzaki Transform Decomposition Method (DETDM). This method is a combination of the Double ELzaki Transform and Adomian Decomposition Method. This technique is hereafter provided and supported with necessary illustrations, together with some attached examples. The results reveal that the new method is very efficient, simple and can be applied to other non-linear problems. 展开更多
关键词 Double Elzaki Transform Adomian Decomposition Method Non-linear Partial differential equations
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Application of Fractional Calculus to a Linear Third Order (Nonhomogeneous and Homogeneous) Ordinary Differential Equation
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作者 李春宜 《Journal of Southeast University(English Edition)》 EI CAS 1999年第2期115-120,共6页
In this paper we apply fractional calculus to solve the 3rd order ordinary differential equation of the following form: (z-a)(z-b)(z-c)φ 3+(βz 2+γz+D)φ 2+(α(2β-3α-3)z+αγ+α(α+1)(a+b+c))φ 1+α(α-... In this paper we apply fractional calculus to solve the 3rd order ordinary differential equation of the following form: (z-a)(z-b)(z-c)φ 3+(βz 2+γz+D)φ 2+(α(2β-3α-3)z+αγ+α(α+1)(a+b+c))φ 1+α(α-1)(β-2α-2)φ=f. 展开更多
关键词 fractional calculus third order differential equation linear NONHOMOGENEOUS HOMOGENEOUS
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Particular Solutions of Generalized Linear Second Differential Equations by Fractional Calculus
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作者 李春宜 《Journal of Southeast University(English Edition)》 EI CAS 1998年第2期101-107,共7页
In this parer, applications of the fractional calculus to the form (Az 2+Bz+C)ψ 2+(Dz+G)ψ 1+Eψ=f and the partial differential equation 2μz 2(Az 2+Bz+C)+(Dz+G)μz+δμ(z,t)=M 2μT 2+NμT, where ψ 1... In this parer, applications of the fractional calculus to the form (Az 2+Bz+C)ψ 2+(Dz+G)ψ 1+Eψ=f and the partial differential equation 2μz 2(Az 2+Bz+C)+(Dz+G)μz+δμ(z,t)=M 2μT 2+NμT, where ψ 1= d ψ d z and ψ 2= d 2ψ d z 2 are presented. 展开更多
关键词 fractional calculus GENERALIZATION HOMOGENEOUS NONHOMOGENEOUS the second order differential equation linear
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The Application of Linear Ordinary Differential Equations
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作者 Haoyang Cui 《Applied Mathematics》 2020年第12期1292-1315,共24页
In this article, we will explore the applications of linear ordinary differential equations (linear ODEs) in Physics and other branches of mathematics, and dig into the matrix method for solving linear ODEs. Although ... In this article, we will explore the applications of linear ordinary differential equations (linear ODEs) in Physics and other branches of mathematics, and dig into the matrix method for solving linear ODEs. Although linear ODEs have a comparatively easy form, they are effective in solving certain physical and geometrical problems. We will begin by introducing fundamental knowledge in Linear Algebra and proving the existence and uniqueness of solution for ODEs. Then, we will concentrate on finding the solutions for ODEs and introducing the matrix method for solving linear ODEs. Eventually, we will apply the conclusions we’ve gathered from the previous parts into solving problems concerning Physics and differential curves. The matrix method is of great importance in doing higher dimensional computations, as it allows multiple variables to be calculated at the same time, thus reducing the complexity. 展开更多
关键词 linear Algebra MATRIX differential equations Electromagnetism PHYSICS
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Parallel Evolutionary Modeling for Nonlinear Ordinary Differential Equations
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作者 Kang Zhuo Liu Pu Kang Li-shan 《Wuhan University Journal of Natural Sciences》 EI CAS 2001年第3期659-664,共6页
We introduce a new parallel evolutionary algorithm in modeling dynamic systems by nonlinear higher-order ordinary differential equations (NHODEs). The NHODEs models are much more universal than the traditional linear ... We introduce a new parallel evolutionary algorithm in modeling dynamic systems by nonlinear higher-order ordinary differential equations (NHODEs). The NHODEs models are much more universal than the traditional linear models. In order to accelerate the modeling process, we propose and realize a parallel evolutionary algorithm using distributed CORBA object on the heterogeneous networking. Some numerical experiments show that the new algorithm is feasible and efficient. 展开更多
关键词 parallel evolutionary algorithm higher-order ordinary differential equation CORBA
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Linearization of Emden Differential Equation via the Generalized Sundman Transformations
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作者 Joel Mvendaga Orverem Yusuf Haruna +1 位作者 Bala Ma’aji Abdulhamid Magaji Yunbunga Adamu 《Advances in Pure Mathematics》 2021年第3期163-168,共6页
The Emden differential equation is one of the most widely studied and challenging nonlinear dynamics equations in literature. It finds applications in various areas of study such as celestial mechanics, fluid mechanic... The Emden differential equation is one of the most widely studied and challenging nonlinear dynamics equations in literature. It finds applications in various areas of study such as celestial mechanics, fluid mechanics, Steller structure, isothermal gas spheres, thermionic currents and so on. Because of the importance of the equation, the method of generalized Sundman transformation (GST) as proposed by Nakpim and Meleshko is used for linearizing the Emden differential equation. The Emden differential equation considered here is a modification of the equation given by Berkovic. The results obtained in this paper imply that the Emden equation cannot be linearized by a point transformation. The general solution of the modified Emden equation is also obtained. 展开更多
关键词 Emden differential equation Second Order Ordinary differential equation Generalized Sundman Transformation linearIZATION
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