Numerical solutions of stochastic Fisher equation to study migration and population behavior in biological invasion

2017 ◽  
Vol 10 (07) ◽  
pp. 1750103 ◽  
Author(s):  
S. Singh ◽  
S. Saha Ray
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Wiener Process ◽  
Finite Difference Scheme ◽  
Numerical Solutions ◽  
Stability And Convergence ◽  
Fisher Equation ◽  
Sample Paths ◽  
Implicit Finite Difference Scheme ◽  
Cylindrical Wiener Process

In this paper, numerical solutions of the stochastic Fisher equation have been obtained by using a semi-implicit finite difference scheme. The samples for the Wiener process have been obtained from cylindrical Wiener process and Q-Wiener process. Stability and convergence of the proposed finite difference scheme have been discussed scrupulously. The sample paths obtained from cylindrical Wiener process and Q-Wiener process have also been shown graphically.

scholarly journals Finite Difference Solution to a Nonlinear Time-Fractional Logistic Model

2021 ◽  
Vol 13 (2) ◽  
pp. 60
Author(s):  
Yuanyuan Yang ◽  
Gongsheng Li
Keyword(s):  
Finite Difference ◽  
Theoretical Analysis ◽  
Difference Scheme ◽  
Logistic Model ◽  
Stability And Convergence ◽  
Numerical Examples ◽  
Implicit Finite Difference Scheme ◽  
Finite Difference Solution ◽  
Implicit Finite Difference ◽  
Convergence Of The Scheme

We set forth a time-fractional logistic model and give an implicit finite difference scheme for solving of the model. The L^2 stability and convergence of the scheme are proved with the aids of discrete Gronwall inequality, and numerical examples are presented to support the theoretical analysis.

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