scholarly journals A reliable numerical algorithm for a fractional model of Fitzhugh-Nagumo equation arising in the transmission of nerve impulses

2019 ◽  
Vol 8 (1) ◽  
pp. 719-727 ◽  
Author(s):  
Amit Prakash ◽  
Hardish Kaur
Keyword(s):  
Error Analysis ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Numerical Algorithm ◽  
Numerical Scheme ◽  
Homotopy Perturbation Method ◽  
Fractional Model ◽  
Homotopy Perturbation ◽  
Nagumo Equation ◽  
Homotopy Polynomials

Abstract The key objective of this paper is to study the fractional model of Fitzhugh-Nagumo equation (FNE) with a reliable computationally effective numerical scheme, which is compilation of homotopy perturbation method with Laplace transform approach. Homotopy polynomials are employed to simplify the nonlinear terms. The convergence and error analysis of the proposed technique are presented. Numerical outcomes are shown graphically to prove the efficiency of proposed scheme.

A new modification of the homotopy perturbation method

2021 ◽  
pp. 095745652199987
Author(s):  
Magaji Yunbunga Adamu ◽  
Peter Ogenyi
Keyword(s):  
Comparative Analysis ◽  
Error Analysis ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Oscillators ◽  
Absolute Error ◽  
New Method ◽  
Optimal Analysis ◽  
Homotopy Perturbation ◽  
Accuracy And Precision

This study proposes a new modification of the homotopy perturbation method. A new parameter alpha is introduced into the homotopy equation in order to improve the results and accuracy. An optimal analysis identifies the parameter alpha, aimed at improving the solutions. A comparative analysis of the proposed method reveals that the new method presents results with higher degree of accuracy and precision than the classic homotopy perturbation method. Absolute error analysis shows the convenience of the proposed method, providing much smaller errors. Two examples are presented: Duffing and Van der pol’s nonlinear oscillators to demonstrate the efficiency, accuracy, and applicability of the new method.

scholarly journals Nonlinearities distribution Laplace transform-homotopy perturbation method

SpringerPlus ◽  
2014 ◽  
Vol 3 (1) ◽  
pp. 594 ◽  
Author(s):  
Uriel Filobello-Nino ◽  
Hector Vazquez-Leal ◽  
Brahim Benhammouda ◽  
Luis Hernandez-Martinez ◽  
Claudio Hoyos-Reyes ◽  
...  
Keyword(s):  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation

scholarly journals Application of he’s fractional derivative and fractional complex transform for time fractional Camassa-Holm equation

2020 ◽  
Vol 24 (5 Part A) ◽  
pp. 3023-3030 ◽  
Author(s):  
Naveed Anjum ◽  
Qura Ain
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Fractal Theory ◽  
Fractional Model ◽  
Fractional Complex Transform ◽  
Homotopy Perturbation ◽  
Holm Equation ◽  
Physical Understanding

In this article He?s fractional derivative is studied for time fractional Camassa-Holm equation. To transform the considered fractional model into a differential equation, the fractional complex transform is used and He?s homotopy perturbation method is adopted to solve the equation. Physical understanding of the fractional complex transform is elucidated by the two-scale fractal theory.

Numerical inversion method for the Laplace transform based on Boubaker polynomials operational matrix

2021 ◽  
Author(s):  
Rachid Belgacem ◽  
Ahmed Bokhari ◽  
Salih Djilali ◽  
Sunil Kumar
Keyword(s):  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Operational Matrix ◽  
Inversion Method ◽  
Numerical Inversion ◽  
Homotopy Perturbation ◽  
Boubaker Polynomials ◽  
The Laplace Transform ◽  
Good Agreement

We investigate through this research the numerical inversion technique for the Laplace transforms cooperated by the integration Boubaker polynomials operational matrix. The efficiency of the presented approach is demonstrated by solving some differential equations. Also, this technique is combined with the standard Laplace Homotopy Perturbation Method. The numerical results highlight that there is a very good agreement between the estimated solutions with exact solutions.

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