On the Instability of Leap-Frog and Crank-Nicolson Approximations of a Nonlinear Partial Differential Equation
From MaRDI portal
Publication:5674357
DOI10.2307/2005246zbMath0258.65092OpenAlexW4233342178MaRDI QIDQ5674357
Publication date: 1973
Full work available at URL: https://doi.org/10.2307/2005246
Related Items
Stability of Pseudospectral and Finite-Difference Methods for Variable Coefficient Problems, On nonlinear instabilities in leap-frog finite difference schemes, Studies in numerical nonlinear instability. II. A new look at \(u_ t+uu_ x=0\), A Simplified Galerkin Method for Hyperbolic Equations, An energy and potential enstrophy conserving numerical scheme for the multi-layer shallow water equations with complete Coriolis force, Grid resonances, focusing and Benjamin-Feir instabilities in leapfrog time discretizations, Global spectral analysis of three-time level integration schemes: focusing phenomenon, Smooth subgrid fields underpin rigorous closure in spatial discretisation of reaction-advection-diffusion PDEs, On modulational instabilities in discretisations of the Korteweg-de Vries equation, Scalable parallel methods for monolithic coupling in fluid-structure interaction with application to blood flow modeling, Effects of numerical anti-diffusion in closed unsteady flows governed by two-dimensional Navier-Stokes equation, Global spectral analysis: review of numerical methods, A linear focusing mechanism for dispersive and non-dispersive wave problems, An iterative starting method to control parasitism for the Leapfrog method, Group velocity interpretation of the stability theory of Gustafsson, Kreiss, and Sundstroem, An implicit scheme for nonlinear evolution equations, Stability analysis of the Crank-Nicolson-leapfrog method with the Robert-Asselin-Williams time filter, Exact analysis of nonlinear instability in a discrete Burgers' equation, Resolution of subgrid microscale interactions enhances the discretisation of nonautonomous partial differential equations, Stabilized Richardson leapfrog scheme in explicit stepwise computation of forward or backward nonlinear parabolic equations, An implicit particle-in-cell method for granular materials, An implicit difference scheme for a moving boundary hyperbolic problem, A numerical energy conserving method for the DNLS equation, Finite difference discretization of the Kuramoto-Sivashinsky equation, Holistic discretization ensures fidelity to Burgers' equation, The weak nonlinear instability of Euler explicit scheme for the convective equation, A systematic approach for correcting nonlinear instabilities: The Lax- Wendroff scheme for scalar conservation laws, Recent developments in IMEX methods with time filters for systems of evolution equations, Runge-Kutta smoother for suppression of computational-mode instability of leapfrog scheme, Parametric excitation of computational modes inherent to leap-frog scheme applied to the Korteweg-de Vries equation, Focusing: A mechanism for instability of nonlinear finite difference equations, Phase error and stability of second order methods for hyperbolic problems. I, A method for the integration in time of certain partial differential equations, SLOW-BURNING INSTABILITIES OF DUFORT–FRANKEL FINITE DIFFERENCING, Analytical and numerical aspects of certain nonlinear evolution equations. III. Numerical, Korteweg-de Vries equation, Stabilized leapfrog scheme run backward in time, and the explicit O(Δ t)2 stepwise computation of ill-posed time-reversed 2D Navier–Stokes equations, Fourier pseudospectral solution of the regularised long wave equation, Dissipative Two-Four Methods for Time-Dependent Problems, On the stability of the nonlinear Schrödinger equation
Cites Work