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February, 2021 From Stepwise Integrations and Low-rank Updates to a Pseudospectral Solution Operator Matrix for the Helmholtz Operator $\frac{d}{dx} a(x) \frac{d}{dx} + c(x)$
Yung-Ta Li, Ping-Hsuan Tsai, Chun-Hao Teng
Taiwanese J. Math. 25(1): 125-154 (February, 2021). DOI: 10.11650/tjm/200802

Abstract

In this study we propose a construction framework utilizing stepwise integrations and the Sherman-Morrison-Woodbury formula to seek pseudospectral integration preconditioning matrices for differential operators. We illustrate this framework through formulating an inverse matrix for the Helmholtz differential operator of the form $\frac{d}{dx} a(x) \frac{d}{dx} + c(x)$. Numerical experiments were conducted to examine the performance of the derived operator. The results show that the inverse matrix is an effective solution operator to numerically solve general second order differential equations.

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Yung-Ta Li. Ping-Hsuan Tsai. Chun-Hao Teng. "From Stepwise Integrations and Low-rank Updates to a Pseudospectral Solution Operator Matrix for the Helmholtz Operator $\frac{d}{dx} a(x) \frac{d}{dx} + c(x)$." Taiwanese J. Math. 25 (1) 125 - 154, February, 2021. https://doi.org/10.11650/tjm/200802

Information

Received: 16 April 2020; Revised: 17 July 2020; Accepted: 12 August 2020; Published: February, 2021
First available in Project Euclid: 24 August 2020

Digital Object Identifier: 10.11650/tjm/200802

Subjects:
Primary: 65F05, 65N12, 74S25

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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Vol.25 • No. 1 • February, 2021
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