An Analysis of Bilinear Transform Polynomial Methods of Inversion of Laplace Transforms
نویسندگان
چکیده
Methods for the numerical inversion of a Laplace transform F(s) which use a special bilinear transformation of s are particularly eeective in many cases and are widely used. The main purpose of this paper is to analyze the convergence and conditioning properties of a special class of such methods, characterized by the use of Lagrange interpolation. The results derived apply both to complex and real inversion, and show that some known inversion methods are in fact in this class.
منابع مشابه
L2-transforms for boundary value problems
In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.
متن کاملOn the Laguerre Method for Numerically Inverting Laplace Transforms
The Laguerre method for numerically inverting Laplace transforms is an old established method based on the 1935 Tricomi-Widder theorem, which shows (under suitable regularity conditions) that the desired function can be represented as a weighted sum of Laguerre functions, where the weights are coefficients of a generating function constructed from the Laplace transform using a bilinear transfor...
متن کاملNumerical Inversion of Laplace Transforms of Probability Distributions
The purpose of this document is to summarize main points of the paper, “Numerical Inversion of Laplace Transforms of Probability Distributions”, and provide R code for the Euler method that is described in the paper. The code is used to invert the Laplace transform of some popular functions. Context Laplace transform is a useful mathematical tool that one must be familiar with, while doing appl...
متن کاملLaplace Transforms for Numericalinversion via Continued
It is often possible to e ectively calculate cumulative distribution functions and other quantities of interest by numerically inverting Laplace transforms. However, to do so it is necessary to compute the Laplace transform values. Unfortunately, convenient explicit expressions for required transforms are often unavailable. In that event, we show that it is sometimes possible to nd continued-fr...
متن کاملAnalytical Solution for Two-Dimensional Coupled Thermoelastodynamics in a Cylinder
An infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. The two-dimensional coupled thermoelastodynamic PDEs are specified based on equations of motion and energy equation, which are uncoupled using Nowacki potential functions. The Laplace integral transform and Bessel-Fourier series are u...
متن کامل