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STUDYING THE FOCAL VALUE OF ORDINARY DIFFERENTIAL EQUATIONS BY NORMAL FORM THEORY
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作者 张琪昌 梁以德 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1995年第9期891-900,共10页
We present a new method to calculate the focal value of ordinary differential equation by applying the theorem defined the relationship between the normal form and focal value,with the help of a symbolic computation l... We present a new method to calculate the focal value of ordinary differential equation by applying the theorem defined the relationship between the normal form and focal value,with the help of a symbolic computation language M ATHEMATICA,and extending the matrix representation method.This method can be used to calculate the focal value of any high order terms.This method has been verified by an example.The advantage of this method is simple and more readily applicable.the result is directly obtained by substitution. 展开更多
关键词 normal form ordinary differential equation focal value MATHEMATICA
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SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR QUASILINEAR HIGHER ORDINARY DIFFERENTIAL EQUATION
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作者 林宗池 林苏榕 《Acta Mathematica Scientia》 SCIE CSCD 1992年第1期98-112,共15页
In this paper we study the singular perturbation of boundary value problems with perturbations both in the operator and in the interval ends. So as to prove the existence and uniqueness of solution of perturbed proble... In this paper we study the singular perturbation of boundary value problems with perturbations both in the operator and in the interval ends. So as to prove the existence and uniqueness of solution of perturbed problem, to establish the asymptotic expression involving three parameters. Thus, the iterative equation of finding the asymptotic solution is derived and the estimation of the remainder term is given out. We extend results of [l]-[5]. 展开更多
关键词 BVP 十玄 SINGULAR PERTURBATION OF BOUNDARY value PROBLEM FOR QUASILINEAR HIGHER ordinary DIFFERENTIAL EQUATION
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UNIQUENESS OF SOLUTIONS OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR THIRD QRDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS
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作者 赵为礼 《Acta Mathematica Scientia》 SCIE CSCD 1992年第3期304-307,共4页
By making use of the differential inequalities, in this paper we study the uniqueness of solutions of the two kinds of the singularly perturbed boundary value problems for the nonlinear third order ordinary differenti... By making use of the differential inequalities, in this paper we study the uniqueness of solutions of the two kinds of the singularly perturbed boundary value problems for the nonlinear third order ordinary differential equation with a small parameter ε>0: where i=1, 2; a(?)(ε), β(ε) and γ(ε) are functions defined on (0, ε_o], while ε_o>0 is a constant.This paper is the continuation of our works [4, 6]. 展开更多
关键词 UNIQUENESS OF SOLUTIONS OF SINGULARLY PERTURBED BOUNDARY value PROBLEMS FOR THIRD QRDER NONLINEAR ordinary DIFFERENTIAL EQUATIONS BVP
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A CHEBYSHEV-GAUSS SPECTRAL COLLOCATION METHOD FOR ORDINARY DIFFERENTIAL EQUATIONS 被引量:2
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作者 Xi Yang 《Journal of Computational Mathematics》 SCIE CSCD 2015年第1期59-85,共27页
In this paper, we introduce an efficient Chebyshev-Gauss spectral collocation method for initial value problems of ordinary differential equations. We first propose a single interval method and analyze its convergence... In this paper, we introduce an efficient Chebyshev-Gauss spectral collocation method for initial value problems of ordinary differential equations. We first propose a single interval method and analyze its convergence. We then develop a multi-interval method. The suggested algorithms enjoy spectral accuracy and can be implemented in stable and efficient manners. Some numerical comparisons with some popular methods are given to demonstrate the effectiveness of this approach. 展开更多
关键词 Initial value problems of ordinary differential equations Chebyshev-Gaussspectral collocation method Spectral accuracy.
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