• Bulletin of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.521-530
• /
• 1996

This paper treats the existence of odd solutions of the Cauchy problem for a perturbation of a conservation law.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.27 no.4
• /
• pp.207-231
• /
• 2023

This paper aims to improve the alternative formulation of the fifth- and sixth-order accurate weighted essentially non-oscillatory (AWENO) finite difference schemes. The first is to derive the AWENO scheme with sixth-order accuracy in the smooth region of the solution. Second, a new weighted polynomial functions combining the perturbed forms with conserved variable to the AWENO is constructed; the new form of tunable functions are invented to maintain non-oscillatory property. Detailed numerical experiments are presented to illustrate the behavior of the new perturbational AWENO schemes. The performance of the present scheme is evaluated in terms of accuracy and resolution of discontinuities using a variety of one and two-dimensional test cases. We show that the resulted perturbational AWENO schemes can achieve fifth- and sixth-order accuracy in smooth regions while reducing numerical dissipation significantly near singularities.