metadata/DAESCAN00.json

{
  "id": "DAESCAN00",
  "url": "https://www.bmtdynamics.org/cgi-bin/display.pl?name=DAESCAN00",
  "title": "Verified High-Order Integration of DAEs and Higher-order ODEs",
  "pdfs": [
    {
      "url": "https://www.bmtdynamics.org/pub/papers/DAESCAN00/DAESCAN00.pdf",
      "filename": "DAESCAN00.pdf",
      "size_bytes": null
    }
  ],
  "page_text": "Publications\nReprint Server\nVerified High-Order Integration of DAEs and Higher-order ODEs\nAbstract\nWithin the framework of Taylor models, no fundamental difference\n  exists between the antiderivation and the more standard elementary\n  operations. Indeed, a Taylor model for the antiderivative of another\n  Taylor model is straightforward to compute and trivially satisfies\n  inclusion monotonicity.\nThis observation leads to the possibility of treating implicit ODEs\n  and, more importantly, DAEs within a fully Differential Algebraic\n  context, i.e. as implicit equations made of conventional functions\n  as well as the antiderivation. To this end, the highest derivative\n  of the solution function occurring in either the ODE or the\n  constraint conditions of the DAE is represented by a Taylor model.\n  All occurring lower derivatives are represented as antiderivatives\n  of this Taylor model.\nBy rewriting this derivative-free system in a fixed point form, the\n  solution can be obtained from a contracting Differential Algebraic\n  operator in a finite number of steps. Using Schauder's Theorem, an\n  additional verification step guarantees containment of the exact\n  solution in the computed Taylor model. As a by-product, we obtain\n  direct methods for the integration of higher order ODEs. The\n  performance of the method is illustrated through examples.\nJ. Hoefkens, M. Berz, K. Makino, in\n\"Scientific Computing, Validated Numerics and Interval Methods\"\n, W. Kraemer, J. W. v. Gudenberg (Eds.) (2001) Kluwer\nDownload\nClick on the icon to download the corresponding file.\nDownload Postscript version (113421 Bytes).\nDownload Adobe PDF version (104121 Bytes).\nGo Back\nto the reprint server.\nGo Back\nto the home page.\nThis page is maintained by\nKyoko Makino\n. Please contact her if there are any problems with it."
}