scholarly journals Approximate analytic solution of (2+1) dimensional coupled differential Burger’s equation using Elzaki Homotopy Perturbation Method

2016 ◽  
Vol 55 (2) ◽  
pp. 1817-1826 ◽  
Author(s):  
Muhammad Suleman ◽  
Qingbiao Wu ◽  
Ghulam Abbas
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Analytic Solution ◽  
Approximate Analytic Solution ◽  
Burger's Equation ◽  
Homotopy Perturbation ◽  
Burger’S Equation

scholarly journals The Approximate Analytic Solution of the Time-Fractional Black-Scholes Equation with a European Option Based on the Katugampola Fractional Derivative

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 214
Author(s):  
Sivaporn Ampun ◽  
Panumart Sawangtong
Keyword(s):  
Fractional Derivative ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Analytic Solution ◽  
Analytic Solutions ◽  
Approximate Analytic Solution ◽  
European Option ◽  
European Option Pricing ◽  
Homotopy Perturbation ◽  
Black Scholes

In the finance market, it is well known that the price change of the underlying fractal transmission system can be modeled with the Black-Scholes equation. This article deals with finding the approximate analytic solutions for the time-fractional Black-Scholes equation with the fractional integral boundary condition for a European option pricing problem in the Katugampola fractional derivative sense. It is well known that the Katugampola fractional derivative generalizes both the Riemann–Liouville fractional derivative and the Hadamard fractional derivative. The technique used to find the approximate analytic solutions of the time-fractional Black-Scholes equation is the generalized Laplace homotopy perturbation method, the combination of the generalized Laplace transform and homotopy perturbation method. The approximate analytic solution for the problem is in the form of the generalized Mittag-Leffler function. This shows that the generalized Laplace homotopy perturbation method is one of the most effective methods to construct approximate analytic solutions of the fractional differential equations. Finally, the approximate analytic solutions of the Riemann–Liouville and Hadamard fractional Black-Scholes equation with the European option are also shown.

scholarly journals A Multi-Stage Homotopy Perturbation Method for the Fractional Lotka-Volterra Model

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1330
Author(s):  
Martin P. Arciga-Alejandre ◽  
Jorge Sanchez-Ortiz ◽  
Francisco J. Ariza-Hernandez ◽  
Gabriel Catalan-Angeles
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Analytic Solution ◽  
Volterra Model ◽  
Order Of Accuracy ◽  
Homotopy Perturbation ◽  
Multi Stage ◽  
The Stability ◽  
Derivative Order

In this work, we propose an efficient multi-stage homotopy perturbation method to find an analytic solution to the fractional Lotka-Volterra model. We obtain its order of accuracy, and we study the stability of the system. Moreover, we present several examples to show of the effectiveness of this method, and we conclude that the value of the derivative order plays an important role in the trajectories velocity.

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

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