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Numerical solutions of random mean square Fisher‐KPP models with advection
Author(s) -
Casabán María Consuelo,
Company Rafael,
Jódar Lucas
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5942
Subject(s) - mathematics , discretization , logarithm , square (algebra) , mean square , numerical analysis , nonlinear system , norm (philosophy) , multivariate random variable , random field , mathematical analysis , random walk , random variable , statistics , geometry , physics , quantum mechanics , political science , law
This paper deals with the construction of numerical stable solutions of random mean square Fisher‐Kolmogorov‐Petrosky‐Piskunov (Fisher‐KPP) models with advection. The construction of the numerical scheme is performed in two stages. Firstly, a semidiscretization technique transforms the original continuous problem into a nonlinear inhomogeneous system of random differential equations. Then, by extending to the random framework, the ideas of the exponential time differencing method, a full vector discretization of the problem addresses to a random vector difference scheme. A sample approach of the random vector difference scheme, the use of properties of Metzler matrices and the logarithmic norm allow the proof of stability of the numerical solutions in the mean square sense. In spite of the computational complexity, the results are illustrated by comparing the results with a test problem where the exact solution is known.