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Runge-Kutta and hermite collocation for a biological invasion problem modeled by a generalized fischer equation

Saridakis Ioannis, Papadopoulou Eleni, Athanasakis Ioannis

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URIhttp://purl.tuc.gr/dl/dias/CE6F7BD6-4C9A-45A8-9B28-8B1FB850384F-
Identifierhttp://www.tuc.gr/fileadmin/users_data/amcl-thalis/Images_PDFs/ICMSQUARE_FISCHER.pdf-
Languageen-
Extent4 pgesen
TitleRunge-Kutta and hermite collocation for a biological invasion problem modeled by a generalized fischer equationen
CreatorSaridakis Ioannisen
CreatorΣαριδακης Ιωαννηςel
CreatorPapadopoulou Elenien
CreatorΠαπαδοπουλου Ελενηel
CreatorAthanasakis Ioannisen
CreatorΑθανασακης Ιωαννηςel
Content Summary Fisher’s equation has been widely used to model the biological invasion of single- species communities in homogeneous one dimensional habitats. In this study we develop high order numerical methods to accurately capture the spatiotemporal dynamics of the generalized Fisher equation, a nonlinear reaction-diffusion equation characterized by density dependent non-linear diffusion. Working towards this direction we consider strong stability preserving Runge-Kutta (RK) temporal discretization schemes coupled with the Hermite cubic Collocation (HC) spatial discretization method. We investigate their convergence and stability properties to reveal efficient HC-RK pairs for the numerical treatment of the generalized Fisher equation. The Hadamard product is used to characterize the collocation discretized non linear equation terms as a first step for the treatment of generalized systems of relevant equations. Numerical experimentation is included to demonstrate the performance of the methods.en
Type of ItemΠλήρης Δημοσίευση σε Συνέδριοel
Type of ItemConference Full Paperen
Licensehttp://creativecommons.org/licenses/by/4.0/en
Date of Item2015-10-16-
Date of Publication2013-
Bibliographic Citation I.E. Athanassakis, E.P. Papadopoulou , Y. G. Saridakis.(2013).Runge-Kutta and hermite collocation for a biological invasion problem modeled by a generalized fischer equation.Presented at 2nd International Conference on Mathematical Modeling in Physical Sciences .[online].Available:http://www.tuc.gr/fileadmin/users_data/amcl-thalis/Images_PDFs/ICMSQUARE_FISCHER.pdfen

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