scholarly journals Dynamical Computations of the FitzHugh- Nagumo Equation

2021 ◽  
pp. 027-036
Author(s):  
Onyejekwe Okey Oseloka
Keyword(s):  
Nagumo Equation

Higher order accurate numerical solution of Nagumo equation

2021 ◽  
Author(s):  
Sobin Thomas ◽  
Gopika P. B. ◽  
Suresh Kumar Nadupuri
Keyword(s):  
Numerical Solution ◽  
Higher Order ◽  
Nagumo Equation ◽  
Accurate Numerical Solution

On a new modified fractional analysis of Nagumo equation

2019 ◽  
Vol 12 (03) ◽  
pp. 1950034 ◽  
Author(s):  
Khaled M. Saad ◽  
Si̇nan Deni̇z ◽  
Dumi̇tru Baleanu
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Convergence Analysis ◽  
Fractional Derivatives ◽  
Transform Method ◽  
Average Residual ◽  
Homotopy Analysis ◽  
Fractional Analysis ◽  
Nagumo Equation ◽  
Modified Equation

In this work, a new modified fractional form of the Nagumo equation has been presented and deeply analyzed. Using the Caputo–Fabrizio and Atangana–Baleanu time-fractional derivatives, classical Nagumo model is transformed to a new fractional version. The modified equation has been solved by using the homotopy analysis transform method. The convergence analysis has been also examined with the help of the so-called [Formula: see text]-curves and average residual error. Comparing the obtained approximate solution with the exact solution leaves no doubt believing that the proposed technique is very efficient and converges toward the exact solution very rapidly.

scholarly journals Abundant distinct types of solutions for the nervous biological fractional FitzHugh–Nagumo equation via three different sorts of schemes

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abdel-Haleem Abdel-Aty ◽  
Mostafa M. A. Khater ◽  
Dumitru Baleanu ◽  
E. M. Khalil ◽  
Jamel Bouslimi ◽  
...  
Keyword(s):  
Nervous System ◽  
Expansion Method ◽  
B Spline ◽  
Stability Behavior ◽  
Nerve Impulses ◽  
Dynamical Behaviors ◽  
Different Types ◽  
Nagumo Equation ◽  
The Stability

Abstract The dynamical attitude of the transmission for the nerve impulses of a nervous system, which is mathematically formulated by the Atangana–Baleanu (AB) time-fractional FitzHugh–Nagumo (FN) equation, is computationally and numerically investigated via two distinct schemes. These schemes are the improved Riccati expansion method and B-spline schemes. Additionally, the stability behavior of the analytical evaluated solutions is illustrated based on the characteristics of the Hamiltonian to explain the applicability of them in the model’s applications. Also, the physical and dynamical behaviors of the gained solutions are clarified by sketching them in three different types of plots. The practical side and power of applied methods are shown to explain their ability to use on many other nonlinear evaluation equations.

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