4 papers
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…
A third-order finite difference weighted essentially non-oscillatory scheme with shallow neural network
Kwanghyuk Park, Xinjuan Chen, Dongjin Lee +2
In this paper, we introduce the finite difference weighted essentially non-oscillatory (WENO) scheme based on the neural network for hyperbolic conservation laws. We employ the sup…
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…
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…