TY - JOUR
T1 - New Finite-Volume Relaxation Methods for the Third-Order Differential Equations
AU - Fayssal Benkhaldoun & Mohammed Seaïd
JO - Communications in Computational Physics
VL - 4
SP - 820
EP - 837
PY - 2008
DA - 2008/04
SN - 4
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cicp/7816.html
KW - 
AB - <p style="text-align: justify;">We propose a new method for numerical solution of the third-order differential equations. The key idea is to use relaxation approximation to transform the nonlinear third-order differential equation to a semilinear second-order differential system
with a source term and a relaxation parameter. The relaxation system has linear characteristic variables and can be numerically solved without relying on Riemann problem
solvers or linear iterations. A non-oscillatory finite volume method for the relaxation
system is developed. The method is uniformly accurate for all relaxation rates. Numerical results are shown for some nonlinear problems such as the Korteweg-de Vires
equation. Our method demonstrated the capability of accurately capturing soliton
wave phenomena.</p>