共查询到20条相似文献，搜索用时 31 毫秒
1.
胡轶 《太原教育学院学报》2007,(2)
通过研究Laplace变换在初值问题中的应用,且拟解决线性微分方程的初值问题。我们知道Laplace变换求解初值问题比其他方法条件宽泛方便。用Laplace变换法可把原函数所遵从的常系数微分方程变成像函数所遵从的代数方程来进行求解;把偏微分方程变成常系数微分方程,然后进行求解。 相似文献
2.
胡轶 《太原大学教育学院学报》2007,25(2):88-91
通过研究Laplace变换在初值问题中的应用,且拟解决线性微分方程的初值问题。我们知道Laplace变换求解初值问题比其他方法条件宽泛方便。用Laplace变换法可把原函数所遵从的常系数微分方程变成像函数所遵从的代数方程来进行求解;把偏微分方程变成常系数微分方程,然后进行求解。 相似文献
3.
李广全 《天津职业院校联合学报》2007,9(5):76-79
介绍拉氏变换的定义、单位阶跃函数及单位脉冲函数,研究单位阶跃函数与单位脉冲函数的关系,并结合使用拉氏变换容易产生的错误,进一步研究单位脉冲函数的性质及其作用,有助于拉氏变换的正确使用。 相似文献
4.
Delta function is an important function in mathematics and physics. In this paper, the Laplace transforms of δ(t)and δ(t-τ)have been discussed in detail. After the Laplace transform of δ(t)is analyzed, the author has found that three aspects should be taken into account, i.e. τ→0+, τ→0- andτ=0; and it is the same with the Laplace transform of δ(t-τ). Then the results of the Laplace transform of Delta function have been obtained in a rigorous and comprehensive sense. 相似文献
5.
邱筝 《南通职业大学学报》2009,23(4):106-108
介绍了Mathematica软件中Fourier变换、Laplace变换及其逆变换的基本指令,通过用Mathematica求解线性微分方程、线性微分方程组和基本电路等实例阐述了数学软件包Mathematica在积分变换教学中的具体用法。实践表明,Mathematica作为辅助教学和计算工具,可降低计算难度,提高教学效率。 相似文献
6.
考虑了一类由M／M／1队列驱动的流排队模型,其中的输入过程是一马氏调节率过程．通过概率结构的分析,构建了模型的微分方程．运用拉氏变换和连分数的方法求得了缓冲器容量的稳态分布． 相似文献
7.
An operational calculus is outlined that enables the determination of the response of any lumped circuit to a general waveform. It is based on elementary notions of operator algebra (sum, product, and inversion of operators) and is rigorously deducible. All processes are carried out in the time domain, no transform or complex-variable theory being needed. The operators turn out to correspond to superposition integrals of impulse responses. Steady-state theory is derived easily as a special case. In particular, the response to any periodic waveform can be calculated by integrations over a single period and is a distinct improvement over the use of Fourier series or Laplace transforms for this problem. The analog of the calculus in the frequency domain is shown to correspond to the use of the bilateral Laplace transformation. 相似文献
8.
综述生灭过程中的构造以及此类过程的积分型泛函的分布.当过程中断时,构造出全部过程,证明全体生灭过程与全体特征数列间存在一一对应.研究依赖于过程的轨道的积分型泛函,给出这种泛函分布的Laplace变换的递推关系,特别,对停留时求出其分布函数的表达式. 相似文献
9.
Mitrajyoti Ghosh 《Resonance》2016,21(11):1029-1042
In this article we shall mathematically analyse the Resistor-Capacitor (RC) circuit with the help of Fourier transforms (FT). This very general technique gives us a lot of insight into solving first order differential equations with source terms depending on time. In itself, the RC circuit is by far the most commonplace entity in modern electronics. But the method of FT is not the accepted custom for an electronic engineer, who is probably more comfortable working with complex impedances and phasors while solving problems in network analysis. In fact, what is used much more extensively is the Laplace transform. But a lot of things, (including the complex impedance itself, and some insight into complex analysis) can be understood better if we use the FT approach to solve the differential equations that come up in network analysis. The use of FT comes smoothly from first principles — precisely what we set out to demonstrate here. 相似文献
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11.
INTRODUCTIONBiot’sconsolidationtheorywasproposedin1 941fromcontinuousmediumfundamentalequations.Thetheorytakingintoaccountthecouplingbetweenthesolidstrainsandporepres suredissipationiscalled“coupledconsolidationtheory” .Thesolutionofgoverningequationso… 相似文献
12.
本文以三种不同的方法即矩阵法、快速傅立叶变换法和拉普拉斯变换法分别求出振动系统的简振频率．并将拉普拉斯变换法得出的系统的微分方程的解析通过MATLAB动态仿真。 相似文献
13.
Axisymmetric fundamental solutions that are applied in the consolidation calculations of a finitecaly clay layer with impeded
boundaries were derived. Laplace and Hankel integral transforms were utilized with respect to time and radial coordinates,
respectively in the analysis. The derivation of fundamental solutions considers two boundary-value problems involving unit
point loading and ring loading in the vertical. The solutions are extended to circular distributed and strip distributed normal
load. The computation and analysis of settlements, vertical total stress and excess pore pressure in the consolidation layer
subject to circular loading are presented.
Project (No. 500117) supported by the National Natural Science Foundation of Zhejiang Province 相似文献
14.
吴专保 《岳阳职业技术学院学报》2007,22(2):69-72
x方向采用有限元法,t方向用拉普拉斯的数值逆,求解一个偏积分微分方程的数值解,简便易行,而且该方法选择适当的求导阶数n可以达到所要求的精度。 相似文献
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16.
申洪 《赣南师范学院学报》1988,(Z1)
本文是用连分式求解离散Master方程。我们仅限于考虑一个自变量的情况,并让转移速率W(n+2,n)≠0,W(n-2,n)=0。利用Laplace变换和逆变换,我们求出了这种限制下的两“粒子”跳跃离散Master方程的与时间有关的严格解,它服从一些循环关系。 相似文献
17.
In this paper,a model named fictitious soil pile was introduced to solve the boundary coupled problem at the pile tip.In the model,the soil column between pile tip and bedrock was treated as a fictitious pile,which has the same properties as the local soil.The tip of the fictitious soil pile was assumed to rest on a rigid rock and no tip movement was allowed.In combination with the plane strain theory,the analytical solutions of vertical vibration response of piles in a frequency domain and the corresponding semi-analytical solutions in a time domain were obtained using the Laplace transforms and inverse Fourier transforms.A parametric study of pile response at the pile tip and head showed that the thickness and layering of the stratum between pile tip and bedrock have a significant influence on the complex impedances.Finally,two applications of the analytical model were presented.One is to identify the defects of the pile shaft,in which the proposed model was proved to be accurate to identify the location as well as the length of pile defects.Another application of the model is to identify the sediment thickness under the pile tip.The results showed that the sediment can lead to the decrease of the pile stiffness and increase of the damping,especially when the pile is under a low frequency load. 相似文献
18.
In this paper,a model named fictitious soil pile was introduced to solve the boundary coupled problem at the pile tip.In the model,the soil column between pile tip and bedrock was treated as a fictitious pile,which has the same properties as the local soil.The tip of the fictitious soil pile was assumed to rest on a rigid rock and no tip movement was allowed.In combination with the plane strain theory,the analytical solutions of vertical vibration response of piles in a frequency domain and the corresponding semi-analytical solutions in a time domain were obtained using the Laplace transforms and inverse Fourier transforms.A parametric study of pile response at the pile tip and head showed that the thickness and layering of the stratum between pile tip and bedrock have a significant influence on the complex impedances.Finally,two applications of the analytical model were presented.One is to identify the defects of the pile shaft,in which the proposed model was proved to be accurate to identify the location as well as the length of pile defects.Another application of the model is to identify the sediment thickness under the pile tip.The results showed that the sediment can lead to the decrease of the pile stiffness and increase of the damping,especially when the pile is under a low frequency load. 相似文献
19.
吴忠怀 《湖南科技学院学报》2009,30(4)
给出了数值求解一类偏积分微分方程的一种全离散格式.在空间x方向一种采用六点隐格式,时间t方向都用拉普拉斯的数值逆求解.得出数值解的精度较高,计算也比较简便. 相似文献
20.
给出了数值求解一类偏微分方程的两种全离散格式。x方向一种采用Legendre谱方法,第二种采用Galerkin谱方法,t方向用拉普拉斯的数值逆求解。第二种方法更具有可操作性,精度高,便于理论分析的优点. 相似文献