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An Analytical Method for Computing the One-Dimensional Backward Wave Problem

Chein-ShanLiu1
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan. E-mail: liucs@ntu.edu.tw

Computers, Materials & Continua 2009, 13(3), 219-234. https://doi.org/10.3970/cmc.2009.013.219

Abstract

The present paper reveals a new computational method for the illposed backward wave problem. The Fourier series is used to formulate a first-kind Fredholm integral equation for the unknown initial data of velocity. Then, we consider a direct regularization to obtain a second-kind Fredholm integral equation. The termwise separable property of kernel function allows us to obtain an analytical solution of regularization type. The sufficient condition of the data for the existence and uniqueness of solution is derived. The error estimate of the regularization solution is provided. Some numerical results illustrate the performance of the new method.

Keywords

Wave equation, Backward wave problem, Fourier series, Regularization solution, Error estimate, Separable kernel

Cite This Article

. and . , "An analytical method for computing the one-dimensional backward wave problem," Computers, Materials & Continua, vol. 13, no.3, pp. 219–234, 2009.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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