A high-order implicit–explicit Runge–Kutta type scheme for the numerical solution of the Kuramoto–Sivashinsky equation

DOI10.1080/00207160.2020.1814262OpenAlexW3081345820MaRDI QIDQ5031323

No author found.

Publication date: 18 February 2022

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.12183

zbMATH Keywords

Kuramoto-Sivashinsky equationexponential time differencingcompact finite differenceimplicit-explicit schemepartial fraction splitting technique

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (4)

Numerical simulation of high-dimensional two-component reaction–diffusion systems with fractional derivatives ⋮ Study of \(4^{th}\) order Kuramoto-Sivashinsky equation by septic Hermite collocation method ⋮ Convergence of a finite difference scheme for a flame/smoldering-front evolution equation and its application to wavenumber selection ⋮ Solitary wave propagation of the generalized Kuramoto-Sivashinsky equation in fragmented porous media

Cites Work

• Higher order exponential time differencing scheme for system of coupled nonlinear Schrödinger equations
• Exponential time differencing for stiff systems
• Generalized integrating factor methods for stiff PDEs
• Quintic B-spline collocation method for numerical solution of the Kuramoto-Sivashinsky equation
• A spectral method for the time evolution in parabolic problems
• Numerical solutions of the generalized Kuramoto-Sivashinsky equation by Chebyshev spectral collocation methods
• Implementation of exponential Rosenbrock-type integrators
• A mesh-free numerical method for solution of the family of Kuramoto-Sivashinsky equations
• The Kuramoto-Sivashinsky equation: a bridge between PDE's and dynamical systems
• Second-order splitting combined with orthogonal cubic spline collocation method for the Kuramoto-Sivashinsky equation
• Compact finite difference schemes with spectral-like resolution
• Finite difference discretization of the Kuramoto-Sivashinsky equation
• A new class of time discretization schemes for the solution of nonlinear PDEs
• Efficient lattice Boltzmann models for the Kuramoto-Sivashinsky equation
• Time discretization and stability regions for dissipative-dispersive Kuramoto-Sivashinsky equation arising in turbulent gas flow over laminar liquid
• A fast spectral algorithm for nonlinear wave equations with linear dispersion
• Dissipative solitons
• A second-order exponential time differencing scheme for non-linear reaction-diffusion systems with dimensional splitting
• The locally extrapolated exponential time differencing LOD scheme for multidimensional reaction-diffusion systems
• Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations
• Numerical solutions of the generalized kuramoto-sivashinsky equation using B-spline functions
• On solitary waves running down an inclined plane
• A Fourier-Series Method for Solving Soliton Problems
• On Restart and Error Estimation for Krylov Approximation of $w=f(A)v$
• Wave formation on vertical falling liquid films
• Viscoelastic behaviour of cellular solutions to the Kuramoto-Sivashinsky model
• Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• Fourth-Order Time-Stepping for Stiff PDEs
• Long Waves on Liquid Films
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A high-order implicit–explicit Runge–Kutta type scheme for the numerical solution of the Kuramoto–Sivashinsky equation