Positivity preserving stochastic θ-methods for selected SDEs

2021 ◽  
Author(s):  
Carmela Scalone
Keyword(s):  
Positivity Preserving

scholarly journals Positivity preserving high order schemes for angiogenesis models

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Carpio ◽  
E. Cebrian
Keyword(s):  
Kinetic Equation ◽  
Time Discretization ◽  
Strong Stability ◽  
High Order ◽  
Angiogenic Factor ◽  
Strong Stability Preserving ◽  
Positivity Preserving ◽  
Blood Vessel Formation ◽  
High Order Schemes ◽  
Asymptotic Reduction

Abstract Hypoxy induced angiogenesis processes can be described by coupling an integrodifferential kinetic equation of Fokker–Planck type with a diffusion equation for the angiogenic factor. We propose high order positivity preserving schemes to approximate the marginal tip density by combining an asymptotic reduction with weighted essentially non oscillatory and strong stability preserving time discretization. We capture soliton-like solutions representing blood vessel formation and spread towards hypoxic regions.

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