The Galerkin method for the KdV equation using a new basis of smooth piecewise cubic polynomials

DOI10.1016/j.amc.2012.02.027zbMath1245.65127OpenAlexW1999750395MaRDI QIDQ440764

Su-Cheol Yi, Shu-Yan Hao, Shu-Sen Xie

Publication date: 19 August 2012

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2012.02.027

zbMATH Keywords

stabilityGalerkin methodconservation lawKdV equationsmooth piecewise cubic polynomial

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (7)

Numerical method for generalized time fractional KdV‐type equation ⋮ Single soliton and double soliton solutions of the quadratic‐nonlinear Korteweg‐de Vries equation for small and long‐times ⋮ Unnamed Item ⋮ A compact-type CIP method for general Korteweg-de Vries equation ⋮ A hybrid numerical method for the KdV equation by finite difference and sinc collocation method ⋮ Modification of quintic B-spline differential quadrature method to nonlinear Korteweg-de Vries equation and numerical experiments ⋮ Numerical solution of a coupled modified Korteweg–de Vries equation by the Galerkin method using quadratic B-splines

Cites Work

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• An analytical numerical method for solving the Korteweg-de Vries equation
• Analytical and numerical aspects of certain nonlinear evolution equations. III. Numerical, Korteweg-de Vries equation
• Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations
• The Fourier pseudospectral method with a restrain operator for the Korteweg-de Vries equation
• A small time solutions for the Korteweg-de Vries equation
• A quintic B-spline finite elements scheme for the KdVB equation
• A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect
• A small time solutions for the Korteweg--de Vries equation using spline approximation
• Numerical solution of Korteweg-de Vries equation by Galerkin B-spline finite element method
• On finite-difference methods for the Korteweg-de Vries equation
• A Legendre--Petrov--Galerkin and Chebyshev Collocation Method for Third-Order Differential Equations
• On Stability of Some Finite Difference Schemes for the Korteweg-de Vries Equation
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• Error analysis for spectral approximation of the Korteweg-de Vries equation
• A numerical and theoretical study of certain nonlinear wave phenomena
• Conservative numerical methods for solitary wave interactions
• Optimal Error Estimates of the Legendre--Petrov--Galerkin Method for the Korteweg--de Vries Equation

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