Fully discrete finite difference schemes for the fractional Korteweg-de Vries equation

KdV equations (Korteweg-de Vries equations) (35Q53) Fractional derivatives and integrals (26A33) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite difference methods for boundary value problems involving PDEs (65N06) Fractional partial differential equations (35R11)

Cites Work

Unnamed Item
Unnamed Item
Convergence of finite difference schemes for the Benjamin-Ono equation
Convergence of a finite difference method for the KdV and modified KdV equations with \(L^2\) data
Hitchhiker's guide to the fractional Sobolev spaces
Ten equivalent definitions of the fractional Laplace operator
On the global well-posedness of the Benjamin-Ono equation
Numerical approximation of the fractional Laplacian via \(hp\)-finite elements, with an application to image denoising
Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
A boundary value problem for the KdV equation: comparison of finite-difference and Chebyshev methods
A numerical method for the Benjamin-Ono equation
Operator splitting methods for generalized Korteweg-de Vries equations
The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves.
On well-posedness for some dispersive perturbations of Burgers' equation
A convergent Crank-Nicolson Galerkin scheme for the Benjamin-Ono equation
A novel and accurate finite difference method for the fractional Laplacian and the fractional Poisson problem
A high-order accurate finite difference scheme for the KdV equation with time-periodic boundary forcing
Two novel linear-implicit momentum-conserving schemes for the fractional Korteweg-de Vries equation
KdV is well-posed in \(H^{-1}\)
The IVP for the dispersion generalized Benjamin-Ono equation in weighted Sobolev spaces
High-order compact schemes for nonlinear dispersive waves
On the Korteweg - de Vries equation: Existence and uniqueness
Convergence of a fully discrete finite difference scheme for the Korteweg–de Vries equation
Convergence of a Higher Order Scheme for the Korteweg--De Vries Equation
A Para-Differential Renormalization Technique for Nonlinear Dispersive Equations
Operator splitting for the KdV equation
Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation
The initial-value problem for the Korteweg-de Vries equation
On the Generalized Benjamin-Ono Equation
GLOBAL WELL-POSEDNESS OF THE BENJAMIN–ONO EQUATION IN H¹(R)
An efficient method to compute solitary wave solutions of fractional Korteweg–de Vries equations
On the unique continuation of solutions to non-local non-linear dispersive equations
Multilevel Monte Carlo Finite Difference Methods for Fractional Conservation Laws with Random Data
Enhanced Existence Time of Solutions to the Fractional Korteweg--de Vries Equation
Numerical Methods for the Fractional Laplacian: A Finite Difference-Quadrature Approach
Discontinuous Galerkin Method for Fractional Convection-Diffusion Equations
Variational formulation for the stationary fractional advection dispersion equation
Error estimates of finite difference schemes for the Korteweg–de Vries equation
Introduction to nonlinear dispersive equations
Operator splitting for the fractional Korteweg‐de Vries equation
Stability and convergence analysis of a Crank-Nicolson Galerkin scheme for the fractional Korteweg-de Vries equation

This page was built for publication: Fully discrete finite difference schemes for the fractional Korteweg-de Vries equation