Finite Range Method of Approximation for Balance Laws in Measure Spaces
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.
Keywords
Cite
@article{arxiv.1409.0766,
title = {Finite Range Method of Approximation for Balance Laws in Measure Spaces},
author = {Piotr Gwiazda and Piotr Orliński and Agnieszka Ulikowska},
journal= {arXiv preprint arXiv:1409.0766},
year = {2015}
}