TY - JOUR

T1 - Determination of Discontinuity Points and the Jump Magnitude of the Original Based on Its Laplace Image

AU - Лебедева, Анастасия Владимировна

AU - Рябов, Виктор Михайлович

PY - 2024/5/20

Y1 - 2024/5/20

N2 - 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.

AB - 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.

KW - discontinuity points of the original

KW - integral Laplace transform

KW - inversion problem

KW - jump of the original

UR - https://www.mendeley.com/catalogue/e75b9bcb-aff6-3e70-85b2-40da42635b5d/

U2 - 10.1134/s1063454124700067

DO - 10.1134/s1063454124700067

M3 - Article

VL - 57

SP - 213

EP - 218

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -