{
  "id": "1409.0766",
  "version": "v1",
  "published": "2014-09-02T15:57:23.000Z",
  "updated": "2014-09-02T15:57:23.000Z",
  "title": "Finite Range Method of Approximation for Balance Laws in Measure Spaces",
  "authors": [
    "Piotr Gwiazda",
    "Piotr Orliński",
    "Agnieszka Ulikowska"
  ],
  "categories": [
    "math.AP",
    "math.NA"
  ],
  "abstract": "In the following paper we reconsider a recently introduced numerical scheme. The method was designed for a wide class of size structured population models as a variation of the Escalator Boxcar Train (EBT) method, which is commonly used in computational biology. The scheme under consideration bases on the kinetic approach and the split-up technique - it approximates a solution by a sum of Dirac measures at each discrete time moment. In the current paper we propose a modification of this algorithm, which prevents (possible) exponential growth of the number of Dirac Deltas approximating the solution. Our approach bases on the finite range approximation of a coefficient which describes birth processes in a population. We provide convergence results, including the convergence speed. Moreover, some results of numerical simulations for several test cases are shown.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-02T15:57:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite range method",
      "balance laws",
      "measure spaces",
      "finite range approximation",
      "escalator boxcar train"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.0766G"
    }
  }
}