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math.NA2025
JS-type and Z-type weights for fourth-order central-upwind weighted essentially non-oscillatory schemes
Jiaxi Gu, Xinjuan Chen, Kwanghyuk Park +1
The central-upwind weighted essentially non-oscillatory (WENO) scheme introduces the downwind substencil to reconstruct the numerical flux, where the smoothness indicator for the d…
math.NA2024
Explicit radial basis function Runge-Kutta methods
Jiaxi Gu, Xinjuan Chen, Jae-Hun Jung
The aim of this paper is to design the explicit radial basis function (RBF) Runge-Kutta methods for the initial value problem. We construct the two-, three- and four-stage RBF Rung…
math.NA2024
A spatial-temporal weight analysis and novel nonlinear weights of weighted essentially non-oscillatory schemes for hyperbolic conservation laws
Xinjuan Chen, Jiaxi Gu, Jae-Hun Jung
In this paper we analyze the weighted essentially non-oscillatory (WENO) schemes in the finite volume framework by examining the first step of the explicit third-order total variat…