8 papers
A Family of Even-Order Central-Upwind WENO Schemes with Averaged Downwind and Novel Global Smoothness Indicators
Jiaxi Gu, Bao-Shan Wang, Wai Sun Don +1
We propose a simple yet effective local smoothness indicator for the downwind stencil in central-upwind weighted essentially non-oscillatory (WENO) schemes of even order for hyperb…
A scaled TW-PINN: A physics-informed neural network for traveling wave solutions of reaction-diffusion equations with general coefficients
Seungwan Han, Kwanghyuk Park, Jiaxi Gu +1
We propose an efficient and generalizable physics-informed neural network (PINN) framework for computing traveling wave solutions of -dimensional reaction-diffusion equations wi…
Conservative approximation-based feedforward neural network for WENO schemes
Kwanghyuk Park, Jiaxi Gu, Jae-Hun Jung
In this work, we present the feedforward neural network based on the conservative approximation to the derivative from point values, for the weighted essentially non-oscillatory (W…
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…
Neural network Approximations for Reaction-Diffusion Equations -- Homogeneous Neumann Boundary Conditions and Long-time Integrations
Eddel Elà Ojeda Avilés, Jae-Hun Jung, Daniel Olmos Liceaga
Reaction-Diffusion systems arise in diverse areas of science and engineering. Due to the peculiar characteristics of such equations, analytic solutions are usually not available an…
A Numerical Study of WENO Approximations to Sharp Propagating Fronts for Reaction-Diffusion Systems
Jiaxi Gu, Daniel Olmos-Liceaga, Jae-Hun Jung
Many reaction-diffusion systems in various applications exhibit traveling wave solutions that evolve on multiple spatio-temporal scales. These traveling wave solutions are crucial…