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http://dx.doi.org/10.5666/KMJ.2021.61.2.309

Conservative Upwind Correction Method for Scalar Linear Hyperbolic Equations  

Kim, Sang Dong (Gyeongbuk Provincial College, Department of Mathematics, University of Wisconsin-Whitewater)
Lee, Yong Hun (Department of Mathematics and Institute of Pure and Applied Mathematics, Jeonbuk National University)
Shin, Byeong Chun (Department of Mathematics, Chonnam National University)
Publication Information
Kyungpook Mathematical Journal / v.61, no.2, 2021 , pp. 309-322 More about this Journal
Abstract
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;
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