The Generalized Fractional-Order Fisher Equation: Stability and Numerical Simulation

被引:1
作者
Inan, Bilge [1 ]
机构
[1] Iskenderun Tech Univ, Fac Engn & Nat Sci, Dept Engn Basic Sci, TR-31200 Hatay, Turkiye
来源
SYMMETRY-BASEL | 2024年 / 16卷 / 04期
关键词
generalized fractional-order Fisher equation; time-fractional equations; exponential finite difference method; conformable fractional derivative; APPROXIMATE;
D O I
10.3390/sym16040393
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
This study examines the stability and numerical simulation of the generalized fractional-order Fisher equation. The equation serves as a mathematical model describing population dynamics under the influence of factors such as natural selection and migration. We propose an implicit exponential finite difference method to solve this equation, considering the conformable fractional derivative. Furthermore, we analyze the stability of the method through theoretical considerations. The method involves transforming the problem into systems of nonlinear equations at each time since our method is an implicit method, which is then solved by converting them into linear equations systems using the Newton method. To test the accuracy of the method, we compare the results obtained with exact solutions and with those available in the literature. Additionally, we examine the symmetry of the graphs obtained from the solution to examine the results. The findings of our numerical simulations demonstrate the effectiveness and reliability of the proposed approach in solving the generalized fractional-order Fisher equation.
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页数:12
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