4,223 research outputs found
A fully-discrete scheme for systems of nonlinear Fokker-Planck-Kolmogorov equations
We consider a system of Fokker-Planck-Kolmogorov (FPK) equations, where the
dependence of the coefficients is nonlinear and nonlocal in time with respect
to the unknowns. We extend the numerical scheme proposed and studied recently
by the authors for a single FPK equation of this type. We analyse the
convergence of the scheme and we study its applicability in two examples. The
first one concerns a population model involving two interacting species and the
second one concerns two populations Mean Field Games
Perturbative Linearization of Reaction-Diffusion Equations
We develop perturbative expansions to obtain solutions for the initial-value
problems of two important reaction-diffusion systems, viz., the Fisher equation
and the time-dependent Ginzburg-Landau (TDGL) equation. The starting point of
our expansion is the corresponding singular-perturbation solution. This
approach transforms the solution of nonlinear reaction-diffusion equations into
the solution of a hierarchy of linear equations. Our numerical results
demonstrate that this hierarchy rapidly converges to the exact solution.Comment: 13 pages, 4 figures, latex2
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