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.
Naldi, G., Cavalli, F., Perugia, I., Discontinuous Galerkin approximation of porous Fisher-Kolmogorov equations, <<COMMUNICATIONS IN APPLIED AND INDUSTRIAL MATHEMATICS>>, 2013; 4 (N/A): N/A-N/A. [doi:10.1685/journal.caim.446] [http://hdl.handle.net/10807/85482]
Discontinuous Galerkin approximation of porous Fisher-Kolmogorov equations
Cavalli, FaustoSecondo
;
2013
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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