共查询到19条相似文献,搜索用时 93 毫秒
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n 阶变系数非线性微分方程零解的稳定性一般说来是比较困难的问题。文献[4]讨论了一类变系数线性微分方程零解稳定性。本文讨论非线性情形。考虑 n 阶非线性微分方程 相似文献
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利用构造法构造二阶变系数线性齐次微分方程及其解,根据这种方法也能求得某些二阶变系数线性齐次微分方程的非零解,并给出了二阶变系数线性齐次微分方程存在非零解的充要条件. 相似文献
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本文利用二阶线性微分方程与一阶微分方程组的等价关系,给出一些新的可积类型。对于更高阶的变系数微分方程,也可以利用类似的方法,构造新的可积类型。 相似文献
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变系数二阶线性微分方程的一个新的可解类型 总被引:19,自引:3,他引:16
通过双变换——未知函数的线性变换和自变量变换 ,将一类变系数线性微分方程化为二阶常系数线性微分方程 ,从而得到变系数二阶线性微分方程的一个新的可解类型 ,推广了著名的二阶 Euler方程 . 相似文献
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本文讨论了 n阶变系数线性微分方程在变量代换下可化为可解方程组的问题 ,把文 [1 ]的二阶情形推广至 n阶情形 ,且例举了三阶情形 . 相似文献
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揭示了二阶变系数线性微分方程和Riccati方程之间的内在联系,证明了在对这两类方程求解时可以相互转化,从而对二阶变系数线性微分方程和Riccati方程的求解提供更多的思路和途径.. 相似文献
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给出一阶线性非齐次微分方程的积分因子解法,避免了常数变易法带来的不便和不自然;给出,n阶常系数非齐次线性微分方程的降阶解法,可以看出,高阶常系数线性非齐次微分方程最终都可以归结为求解一阶线性微分方程,从而避免了待定系数法求非齐次方程特解的繁琐,并最终说明了一般微积分教材中只给出两种类型常系数非齐次线性微分方程的待定系数解法的原因. 相似文献
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The purpose of this paper is to provide an oscillation theorem that can be applied to half-linear differential equations with time-varying coefficients. A parametric curve by the coefficients is focused in order to obtain our theorem. This parametric curve is a generalization of the curve given by the characteristic equation of the second-order linear differential equation with constant coefficients. The obtained theorem is proved by transforming the half-linear differential equation to a standard polar coordinates system and using phase plane analysis carefully. 相似文献
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根据二阶常系数齐次线性微分方程的特征根,利用降阶法,可给出求解一般二阶常系数非齐次线性微分方程的通解公式. 相似文献
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H Gingold 《Journal of Mathematical Analysis and Applications》1975,52(3):546-552
We obtain a necessary condition on the coefficients of a formal power series, which is a formal solution of a nontrivial singular linear differential equation of order k, with analytic coefficients and prove a “uniqueness” theorem for the differential equation. 相似文献
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A. Branquinho 《Journal of Mathematical Analysis and Applications》2009,356(1):242-256
In this paper we characterize sequences of orthogonal polynomials on the unit circle whose corresponding Carathéodory function satisfies a Riccati differential equation with polynomial coefficients, in terms of second order matrix differential equations. In the semi-classical case, a characterization in terms of second order linear differential equations with polynomial coefficients is deduced. 相似文献
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Ireneusz Winnicki Janusz Jasinski Slawomir Pietrek 《Numerical Methods for Partial Differential Equations》2019,35(6):2275-2304
The paper presents an enhanced analysis of the Lax‐Wendroff difference scheme—up to the eighth‐order with respect to time and space derivatives—of the modified‐partial differential equation (MDE) of the constant‐wind‐speed advection equation. The modified equation has been so far derived mainly as a fourth‐order equation. The Π ‐form of the first differential approximation (differential approximation or equivalent equation) derived by expressing the time derivatives in terms of the space derivatives is used for presenting the MDE. The obtained coefficients at higher order derivatives are analyzed for indications of the character of the dissipative and dispersive errors. The authors included a part of the stencil applied for determining the modified differential equation up to the eighth‐order of the analyzed modified differential equation for the second‐order Lax‐Wendroff scheme. Neither the derived coefficients at the space derivatives of order p ∈ (7 – 8) in the modified differential equation for the Lax‐Wendroff difference scheme nor the results of analyses on the basis of these coefficients of the group velocity, phase shift errors, or dispersive and dissipative features of the scheme have been published. The MDEs for 2 two‐step variants of the Lax‐Wendroff type difference schemes and the MacCormack predictor–corrector scheme (see MacCormack's study) constructed for the scalar hyperbolic conservation laws are also presented in this paper. The analysis of the inviscid Burgers equation solution with the initial condition in a form of a shock wave has been discussed on their basis. The inviscid Burgers equation with the source is also presented. The theory of MDE started to develop after the paper of C. W. Hirt was published in 1968. 相似文献
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S. I. Mitrokhin 《Moscow University Mathematics Bulletin》2009,64(3):102-104
A fourth order differential operator with summable coefficients and some boundary conditions is considered. Asymptotics of solutions to a fourth order differential equation is studied. The equation for eigenvalues is also studied and an asymptotics of the eigenvalues of the considered boundary value problem is obtained. 相似文献
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利用初等变换将常系数非齐次线性微分方程组化为由若干个相互独立的高阶常系数非齐次线性微分方程组成的方程组,再利用高阶常系数齐次线性微分方程的特征根法和非齐次方程的待定系数法求该方程组的基本解组及特解,最后通过初等变换求原方程组的基本解组及特解,从而可求出其通解. 相似文献