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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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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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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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ON DETERMINATION OF THE IMPULSIVE SOLUTIONS AND IMPULSIVE PROPERTIES TO LINEAR NON-HOMOGENEOUS MATRIX DIFFERENTIAL EQUATIONS
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作者 Tan Liansheng 《Acta Mathematica Scientia》 SCIE CSCD 2000年第2期261-272,共12页
This note contains three main results.Firstly,a complete solution of the Linear Non-Homogeneous Matrix Differential Equations(LNHMDEs)is presented that takes into account both the non-zero initial conditions of the ps... This note contains three main results.Firstly,a complete solution of the Linear Non-Homogeneous Matrix Differential Equations(LNHMDEs)is presented that takes into account both the non-zero initial conditions of the pseudo state and the nonzero initial conditions of the input.Secondly,in order to characterise the dynamics of the LNHMDEs correctly,some important concepts such as the state,slow state(smooth state)and fast state(impulsive state)are generalized to the LNHMDE case and the solution of the LNHMDEs is separated into the smooth(slow)response and the fast(implusive)response.As a third result,a new characterization of the impulsive free initial conditions of the LNHMDEs is given. 展开更多
关键词 linear matrix differential equation impulsive and smooth solution impulsive free initial conditions {1}-inverse
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THE ESTIMATION OF SOLUTION OF THE BOUNDARY VALUE PROBLEM OF THE SYSTEMS FOR QUASI-LINEAR ORDINARY DIFFERENTIAL EQUATIONS
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作者 黄蔚章 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1992年第8期745-754,共10页
This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equationswhere x,f, y , h, A, B and C all belong to Rn , and g is an n×n matrix ... This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equationswhere x,f, y , h, A, B and C all belong to Rn , and g is an n×n matrix function. Under suitable conditions we prove the existence of the solutions by diagonalization and the fixed point theorem and also estimate the remainder. 展开更多
关键词 systems of the quasi-linear ordinary differential equation singular perturbation DIAGONALIZATION asymptotic expansion
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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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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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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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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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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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Existence and Multiplicities of Solutions for Asymptotically Linear Ordinary Differential Equations Satisfying Sturm-Liouville BVPs with Resonance
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作者 Keqiang Li Ronghua Tong 《Journal of Applied Mathematics and Physics》 2019年第5期1197-1211,共15页
In this paper, we prove existence and multiplicities of solutions for asymptotically linear ordinary differential equations satisfying Sturm-Liouville boundary value conditions with resonance. Adding assumption H3 tha... In this paper, we prove existence and multiplicities of solutions for asymptotically linear ordinary differential equations satisfying Sturm-Liouville boundary value conditions with resonance. Adding assumption H3 that is similar to (LL) in Theorem 1.1, by index theory and Morse theory, we obtain more nontrivial solutions. 展开更多
关键词 Asymptotically linear Ordinary differential equations with RESONANCE Multiple SOLUTIONS STURM-LIOUVILLE Boundary Value Problem Index THEORY Morse THEORY
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Stability analysis of linear multistep methods for neutral delay differential equations
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作者 S K JAFFER 刘明珠 丁效华 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2003年第2期168-170,共3页
The stability analysis of linear multistep (LM) methods is carried out under Kreiss resolvent condition when they are applied to neutral delay differential equations of the form y′(t)=ay(t)+by(t-τ)+ cy′(t- τ) y(t)... The stability analysis of linear multistep (LM) methods is carried out under Kreiss resolvent condition when they are applied to neutral delay differential equations of the form y′(t)=ay(t)+by(t-τ)+ cy′(t- τ) y(t)=g(t) -τ≤t≤0 with τ>0 and a, b and c∈, and it is proved that the ‖B n‖ is suitably bounded, where B is the companion matrix. 展开更多
关键词 linear multistep methods neutral differential equations Kreiss resolvent condition
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Strong Stability Preserving IMEX Methods for Partitioned Systems of Differential Equations
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作者 Giuseppe Izzo Zdzislaw Jackiewicz 《Communications on Applied Mathematics and Computation》 2021年第4期719-758,共40页
We investigate strong stability preserving(SSP)implicit-explicit(IMEX)methods for partitioned systems of differential equations with stiff and nonstiff subsystems.Conditions for order p and stage order q=p are derived... We investigate strong stability preserving(SSP)implicit-explicit(IMEX)methods for partitioned systems of differential equations with stiff and nonstiff subsystems.Conditions for order p and stage order q=p are derived,and characterization of SSP IMEX methods is provided following the recent work by Spijker.Stability properties of these methods with respect to the decoupled linear system with a complex parameter,and a coupled linear system with real parameters are also investigated.Examples of methods up to the order p=4 and stage order q—p are provided.Numerical examples on six partitioned test systems confirm that the derived methods achieve the expected order of convergence for large range of stepsizes of integration,and they are also suitable for preserving the accuracy in the stiff limit or preserving the positivity of the numerical solution for large stepsizes. 展开更多
关键词 Partitioned systems of differential equations SSP property IMEX general linear methods Construction of highly stable methods
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Oscillation Criteria of second Order Non-Linear Differential Equations
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作者 Hishyar Kh. Abdullah 《Open Journal of Applied Sciences》 2012年第4期120-122,共3页
In this paper we are concerned with the oscillation criteria of second order non-linear homogeneous differential equation. Example have been given to illustrate the results.
关键词 component OSCILLATORY SECOND order differential equations Non-linear.
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