A NEW DUAL-PETROV–GALERKIN METHOD FOR THIRD AND HIGHER ODD-ORDER DIFFERENTIAL EQUATIONS: APPLICATION TO THE KDV EQUATION∗

@inproceedings{SIAMJ2003AND,
  title={A NEW DUAL-PETROV–GALERKIN METHOD FOR THIRD AND HIGHER ODD-ORDER DIFFERENTIAL EQUATIONS: APPLICATION TO THE KDV EQUATION∗},
  author={N SIAMJ.},
  year={2003}
}
A new dual-Petrov–Galerkin method is proposed, analyzed, and implemented for third and higher odd-order equations using a spectral discretization. The key idea is to use trial functions satisfying the underlying boundary conditions of the differential equations and test functions satisfying the “dual” boundary conditions. The method leads to linear systems which are sparse for problems with constant coefficients and well conditioned for problems with variable coefficients. Our theoretical… CONTINUE READING

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A Dual-Petrov-Galerkin Method for the Kawahara-Type Equations

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  • 2008
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