Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc.

Published online August 1, 2022

Copyright © The Korean Mathematical Society.

Thomas algorithms for systems of fourth-order finite difference methods

Soyoon Bak, Philsu Kim, and Sangbeom Park

Kyungpook National University

Abstract

The main objective of this paper is to develop a concrete inverse formula of the system induced by the fourth-order finite difference method for two-point boundary value problems with Robin boundary conditions. This inverse formula facilitates to make a fast algorithm for solving the problems. Our numerical results show the efficiency and accuracy of the proposed method, which is implemented by the Thomas algorithm.

Keywords: finite difference method, inverse of tridiagonal matrix, Thomas algorithm, boundary value problem

MSC numbers: 65N06

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