doi: 10.1685/journal.caim.446

Discontinuous Galerkin approximation of porous Fisher-Kolmogorov equations

Giovanni Naldi, Fausto Cavalli, Ilaria Perugia

Abstract


We consider the generalized porous Fisher-Kolmogorov equations, which model several phenomena in population dynamics, as well as in chemical reactions. For these equations, we present new numerical high-order schemes, based on discontinuous Galerkin space discretizations and Runge-Kutta time stepping. These methods are capable to reproduce the main properties of the analytical solutions. We present some preliminary theoretical results and provide several numerical tests.

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Communications in Applied and Industrial Mathematics
ISSN: 2038-0909