Conservative Finite Difference Schemes for the Degasperis-Procesi Equation(Theory)

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  • Miyatake Yuto
    Graduate School of Information Science and Technology, The University of Tokyo
  • Matsuo Takayasu
    Graduate School of Information Science and Technology, The University of Tokyo

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  • Degasperis-Procesi方程式に対する保存則を保つ差分スキーム(理論)
  • Degasperis-Procesi方程式に対する保存則を保つ差分スキーム
  • Degasperis Procesi ホウテイシキ ニ タイスル ホゾンソク オ タモツ サブン スキーム

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Abstract

We consider the Degasperis-Procesi equation, which was recently introduced as a completely integrable shallow water equation. We propose nonlinear and linear finite difference schemes for the equation based on an extended version of the discrete variational derivative method, and show that they preserve two associated invariants at a same time. We also prove the unique solvability of the schemes, and evaluate the schemes numerically.

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