Article
Kyungpook Mathematical Journal 2021; 61(2): 309-322
Published online June 30, 2021
Copyright © Kyungpook Mathematical Journal.
Conservative Upwind Correction Method for Scalar Linear Hyperbolic Equations
Sang Dong Kim, Yong Hun Lee*, Byeong Chun Shin
Gyeongbuk Provincial College, Yecheon 36830, Korea, and Department of Mathematics, University of Wisconsin-Whitewater, Whitewater WI, USA
e-mail : skim@knu.ac.kr
Department of Mathematics and Institute of Pure and Applied Mathematics, Jeonbuk National University, Jeonju 54896, Korea
e-mail : lyh229@jbnu.ac.kr
Department of Mathematics, Chonnam National University, Gwangju 61186, Korea
e-mail : bcshin@jnu.ac.kr
Received: April 19, 2018; Revised: June 1, 2021; Accepted: June 1, 2021
A conservative scheme for solving scalar hyperbolic equations is presented using a quadrature rule and an ODE solver. This numerical scheme consists of an upwind part, plus a correction part which is derived by introducing a new variable for the given hyperbolic equation. Furthermore, the stability and accuracy of the derived algorithm is shown with numerous computations.
Keywords: conservative method, hyperbolic scalar equation, ODE solver, quadrature rule, upwind method