Operator splitting for the KdV equation

Type: Article

Publication Date: 2010-12-29

Citations: 79

DOI: https://doi.org/10.1090/s0025-5718-2010-02402-0

Abstract

We provide a new analytical approach to operator splitting for equations of the type $u_t=Au+B(u)$, where $A$ is a linear operator and $B$ is quadratic. A particular example is the Korteweg–de Vries (KdV) equation $u_t-u u_x+u_{xxx}=0$. We show that the Godunov and Strang splitting methods converge with the expected rates if the initial data are sufficiently regular.

Locations

  • Mathematics of Computation - View - PDF
  • CiteSeer X (The Pennsylvania State University) - View - PDF
  • Mathematics of Computation - View - PDF
  • CiteSeer X (The Pennsylvania State University) - View - PDF

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