A Concise Introduction to Geometric Numerical Integration

2017 ◽  
Author(s):  
Sergio Blanes ◽  
Fernando Casas
Keyword(s):  
Numerical Integration ◽  
Geometric Numerical Integration

scholarly journals Geometric Numerical Integration in Ecological Modelling

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 25 ◽  
Author(s):  
Fasma Diele ◽  
Carmela Marangi
Keyword(s):  
Numerical Integration ◽  
Time Integration ◽  
Continuous Model ◽  
Ecological Models ◽  
Ecological Modelling ◽  
Geometric Numerical Integration ◽  
Qualitative Properties ◽  
Long Time ◽  
Numerical Integrators ◽  
Long Time Integration

A major neglected weakness of many ecological models is the numerical method used to solve the governing systems of differential equations. Indeed, the discrete dynamics described by numerical integrators can provide spurious solution of the corresponding continuous model. The approach represented by the geometric numerical integration, by preserving qualitative properties of the solution, leads to improved numerical behaviour expecially in the long-time integration. Positivity of the phase space, Poisson structure of the flows, conservation of invariants that characterize the continuous ecological models are some of the qualitative characteristics well reproduced by geometric numerical integrators. In this paper we review the benefits induced by the use of geometric numerical integrators for some ecological differential models.

scholarly journals Geometric numerical integration of the assignment flow

2020 ◽  
Vol 36 (3) ◽  
pp. 034003 ◽  
Author(s):  
Alexander Zeilmann ◽  
Fabrizio Savarino ◽  
Stefania Petra ◽  
Christoph Schnörr
Keyword(s):  
Numerical Integration ◽  
Geometric Numerical Integration
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