analytical differential
- analytical differential的基本解释
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解析微分
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First of all,we have given some of the basic concepts of differential equations, described the constant coefficient linear ordinary differential equation solution, for a class of second-order variable coefficient linear ordinary differential equation initial value problem, an approximate solution, the method is first unknown function of a definition for N sub-interval, and then in between each district within a constant coefficient ordinary differential equations similar to the replacement, the solution has been the problem as similar to the original analytical solution, and then gives a detailed second-order change order coefficient of linear homogeneous ordinary differential equation solution examples, the examples of the approximate method proposed in this paper is valid.
首先给出了微分方程的一些基本概念,讲述了常系数线性常微分方程的解法,针对一类二阶变系数线性常微分方程初值问题,提出了一个近似解法,本方法是先对未知函数的一个定义区间作N等分,然后在每一个小区间内用一个常系数常微分方程近似替换,所得到的解作为原问题的近似解析解,随后详细给出了一个求二阶变系数齐次线性常微分方程的解的实例,该实例说明本文提出的近似方法是有效的。
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The paper consists of four chapters:In chaper 1, we introduce the background and signficance, research and actuality on oscillation of functional partial differential equations; we present research subject in this paper;In chaper 2, we discuss oscillatory property of systems of parabolic differential equations with delays and obtain necessary and sufficient conditions for the oscillation of their solutions; we show the difference between oscillatory property of systems of parabolic differential equations with delays and that of systems of partial differential equtions without delays; we explain the main results with examples;In chapter 3, we discuss oscillatory property of systems of functional parabolic differential equations of neutral type; we obtain some sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples;In chapter 4, we discuss oscillatory property of systems of functional hyperbolic differential equations of neutral type; we obtain sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples.
全文共分四章:第一章简要介绍了泛函偏微分方程的振动的背景和意义、对其研究的简单历史和现状,给出了本文的主要研究对象;第二章讨论了一类时滞抛物方程组解的振动性质,获得了判断其所有解振动的一个易于验证的充要条件;指出了这类具有时滞偏差变元的抛物方程组解的振动性质和不具有时滞偏差变元的抛物方程组解的振动性质的差异;并举例对主要结果进行阐明;第三章讨论了一类中立型抛物方程组解的振动性质,获得了在给定的条件下其所有解振动或全振动的若干充分条件;并举例对主要结果进行阐明;第四章讨论了一类中立型双曲方程组解的振动性质,获得了在给定的条件下其所有解振动或全振动的若干充分条件;并举例对主要结果进行阐明。
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The second-order linear homogeneous differential equations in differential equation theory occupies an important position, but the second order differential equation has no general solution method, most of the solutions of these equations is difficult to obtain analytical expressions and even some impossible to obtain the solution of the form, and the second order differential equation solving is divided into homogeneous and inhomogeneous problems.
二阶线性齐次微分方程在微分方程理论中占有重要位置,但二阶变系数微分方程却没有一般的求解方法,大多数这类方程很难求得解的分析表达式甚至有的根本不可能求得其解的分析形式,并且二阶变系数微分方程的求解又分为齐次的和非齐次的问题。
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analytical differential:解析微分
analytic transformation 解析变换 | analytical differential 解析微分 | analytical geometry 分析几何学