根据拉普拉斯图像确定原点的不连续点和跳跃幅度

A. V. Lebedeva, V. M. Ryabov
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引用次数: 0

摘要

摘要 在许多问题中应用积分拉普拉斯变换,可以得到一个相对于所需原点图像的较简单方程。下一步就会出现反演问题(即根据原图的图像找到原图的问题)。通常情况下,这一步无法通过分析来完成,于是就出现了使用近似反演方法的问题。在这种情况下,近似解以图像及其在复半平面上某些点的导数的线性组合形式表示,图像在复半平面上是规则的。然而,与图像不同的是,原图甚至可能存在不连续点。毫无疑问,开发确定原图可能的不连续点以及原图在这些点上的跳变幅度的方法是一项令人感兴趣的任务。所建议的方法意味着使用高阶图像导数值,以获得令人满意的近似解精度。还给出了加速所获近似值收敛的方法。数值实验结果表明了所建议技术的效率。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Determination of Discontinuity Points and the Jump Magnitude of the Original Based on Its Laplace Image

Abstract

The application of the integral Laplace transform to a wide class of problems leads to a simpler equation relative to the image of the desired original. At the next step, the inversion problem (i.e., the problem of finding the original based on its image) arises. As a rule, this step cannot be carried out analytically, and the problem arises of using approximate inversion methods. In this case, the approximate solution is represented in the form of a linear combination between the image and its derivatives at certain points of the complex half-plane, in which the image is regular. Unlike the image, however, the original may have even discontinuity points. Of undoubted interest is the task of developing methods for determining the possible discontinuity points of the original as well as the magnitudes of the original jump at these points. The suggested methods imply using values of high-order image derivatives in order to obtain a satisfactory accuracy of approximate solutions. The methods for accelerating the convergence of the obtained approximations are given. The results of numerical experiments which illustrate the efficiency of the suggested techniques are demonstrated.

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来源期刊
CiteScore
0.70
自引率
50.00%
发文量
44
期刊介绍: Vestnik St. Petersburg University, Mathematics  is a journal that publishes original contributions in all areas of fundamental and applied mathematics. It is the prime outlet for the findings of scientists from the Faculty of Mathematics and Mechanics of St. Petersburg State University. Articles of the journal cover the major areas of fundamental and applied mathematics. The following are the main subject headings: Mathematical Analysis; Higher Algebra and Numbers Theory; Higher Geometry; Differential Equations; Mathematical Physics; Computational Mathematics and Numerical Analysis; Statistical Simulation; Theoretical Cybernetics; Game Theory; Operations Research; Theory of Probability and Mathematical Statistics, and Mathematical Problems of Mechanics and Astronomy.
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