The weak nonlinear instability of Euler explicit scheme for the convective equation
type: Item
instance of: scholarly article
title: The weak nonlinear instability of Euler explicit scheme for the convective equation
zbMATH Open document ID: 0626.65084
DOI: 10.1016/0021-9991(87)90056-8
author: Min Hsia Han
author: Nen Jeng Yih
published in: Journal of Computational Physics
publication date: 1987-01-01T00:00:00Z
review text: The weak nonlinear instability of the Euler explicit difference schemes is considered for the one-dimensional nonlinear convective equation, where the field of velocity is subject to periodic boundary and initial conditions. The problem is studied analytically making use of perturbation expansion and discrete Fourier transform techniques. A short time weak nonlinear growth of Fourier modes for the error is found, provided that the linear stability conditions are satisfied and the maximum growth is approximately proportional to the inverse of the grid spacing.
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4018283
zbMATH Keywords: weak nonlinear instability
zbMATH Keywords: Euler explicit difference schemes
zbMATH Keywords: nonlinear convective equation
zbMATH Keywords: perturbation expansion
zbMATH Keywords: discrete Fourier transform
MaRDI profile type: Publication
full work available at URL: 0021-9991(87)90056-8
OpenAlex ID: W2091017924
cites work: The Stability Properties of a Coupled Pair of Non-Linear Partial Difference Equations
cites work: Q5536978
cites work: On the Instability of Leap-Frog and Crank-Nicolson Approximations of a Nonlinear Partial Differential Equation
cites work: Focusing: A mechanism for instability of nonlinear finite difference equations
cites work: Heuristic stability theory for finite-difference equations
cites work: Multi-Level Adaptive Solutions to Boundary-Value Problems
cites work: Numerical Solution of the Navier-Stokes Equations for a Three-Dimensional Corner
description: scientific article; zbMATH DE number 4018283