A Wachspress-Type Rational Characteristic Method for Solving First-Order Hyperbolic Equations

Authors

Mohamed Al-Lawatia, Department of Mathematics, College of Science, Sultan Qaboos University, P.O. Box 36, Al-Khodh 123, Sultanate of OmanFollow

Abstract

This paper introduces a characteristic method for solving linear first-order hyperbolic partial differential equations in two space dimensions. The algorithm employs rational Wachspress-type basis functions applied to a hexagonal discretization of the domain, integrated within the Eulerian-Lagrangian Localized Adjoint Method (ELLAM) framework. The proposed scheme preserves the strengths of characteristic methods and delivers accurate numerical results, even with large time steps. Computational tests conducted on standard benchmark problems illustrate the effectiveness of the method.

Recommended Citation

Al-Lawatia, Mohamed (2025) A Wachspress-Type Rational Characteristic Method for Solving First-Order Hyperbolic Equations, Sultan Qaboos University Journal For Science: Vol. 30: Iss. 2, 170-178.
DOI: https://doi.org/10.53539/2414-536X.1409
Available at: https://squjs.squ.edu.om/squjs/vol30/iss2/9