Optimal Error Estimates of the Legendre-Petrov-Galerkin Method for the Korteweg-de Vries Equation

@article{Ma2001OptimalEE,
  title={Optimal Error Estimates of the Legendre-Petrov-Galerkin Method for the Korteweg-de Vries Equation},
  author={Heping Ma and Weiwei Sun},
  journal={SIAM J. Numerical Analysis},
  year={2001},
  volume={39},
  pages={1380-1394}
}
In this paper, the Legendre--Petrov--Galerkin method for the Korteweg--de Vries equation with nonperiodic boundary conditions is analyzed. The nonlinear term is computed with the Legendre spectral method and some pseudospectral methods, respectively. Optimal error estimates in L2-norm are obtained for both semidiscrete and fully discrete schemes. The method is also applicable to some (2m+1)th-order differential equations. 

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A New Dual-Petrov-Galerkin Method for Third and Higher Odd-Order Differential Equations: Application to the KDV Equation

  • SIAM J. Numerical Analysis
  • 2003
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