{
  "id": "1303.4116",
  "version": "v1",
  "published": "2013-03-17T22:45:39.000Z",
  "updated": "2013-03-17T22:45:39.000Z",
  "title": "Convergence of Runge-Kutta Methods Applied to Linear Partial Differential-Algebraic Equations",
  "authors": [
    "Kristian Debrabant",
    "Karl Strehmel"
  ],
  "journal": "Applied NumericalMathematics 53 (2005) no. 2-4, pp. 213-229",
  "doi": "10.1016/j.apnum.2004.08.023",
  "categories": [
    "math.NA"
  ],
  "abstract": "We apply Runge-Kutta methods to linear partial differential-algebraic equations of the form $Au_t(t,x) + B(u_{xx}(t,x)+ru_x(t,x))+Cu(t,x) = f(t,x)$, where $A,B,C\\in\\R^{n,n}$ and the matrix $A$ is singular. We prove that under certain conditions the temporal convergence order of the fully discrete scheme depends on the time index of the partial differential-algebraic equation. In particular, fractional orders of convergence in time are encountered. Furthermore we show that the fully discrete scheme suffers an order reduction caused by the boundary conditions. Numerical examples confirm the theoretical results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-17T22:45:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M06",
      "65M20"
    ],
    "keywords": [
      "linear partial differential-algebraic equations",
      "runge-kutta methods",
      "convergence",
      "fully discrete scheme suffers",
      "fully discrete scheme depends"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.4116D"
    }
  }
}