scholarly journals Approximate Solutions of Delay Differential Equations with Constant and Variable Coefficients by the Enhanced Multistage Homotopy Perturbation Method

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
D. Olvera ◽  
A. Elías-Zúñiga ◽  
L. N. López de Lacalle ◽  
C. A. Rodríguez
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Numerical Integration ◽  
Delay Differential Equations ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
Integration Algorithm ◽  
Homotopy Perturbation ◽  
Delay Differential

We expand the application of the enhanced multistage homotopy perturbation method (EMHPM) to solve delay differential equations (DDEs) with constant and variable coefficients. This EMHPM is based on a sequence of subintervals that provide approximate solutions that require less CPU time than those computed from the dde23 MATLAB numerical integration algorithm solutions. To address the accuracy of our proposed approach, we examine the solutions of several DDEs having constant and variable coefficients, finding predictions with a good match relative to the corresponding numerical integration solutions.

scholarly journals Homotopy Perturbation Method for Solving Linear Fuzzy Delay Differential Equations Using Double Parametric Approach

2020 ◽  
Vol 8 (5) ◽  
pp. 551-558 ◽  
Author(s):  
Ali F Jameel ◽  
Sardar G Amen ◽  
Azizan Saaban ◽  
Noraziah H Man ◽  
Fathilah M Alipiah
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Delay Differential Equations ◽  
Homotopy Perturbation Method ◽  
Parametric Approach ◽  
Homotopy Perturbation ◽  
Delay Differential

scholarly journals Approximate Solution of Multi-Term Fractional Order Delay Differential Equations Using Homotopy Perturbation Method

2020 ◽  
Vol 23 (2) ◽  
pp. 60-66
Author(s):  
Mohammed S. Ismael ◽  
◽  
Fadhel S. Fadhel ◽  
Ali Al-Fayadh ◽  
◽  
...  
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Fractional Order ◽  
Delay Differential Equations ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation ◽  
Delay Differential

The Solution of the Variable Coefficients Fourth-Order Parabolic Partial Differential Equations by the Homotopy Perturbation Method

2009 ◽  
Vol 64 (7-8) ◽  
pp. 420-430 ◽  
Author(s):  
Mehdi Dehghan ◽  
Jalil Manafian
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Fourth Order ◽  
Homotopy Perturbation Method ◽  
Variable Coefficients ◽  
Parabolic Partial Differential Equation ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Homotopy Perturbation

AbstractIn this work, the homotopy perturbation method proposed by Ji-Huan He [1] is applied to solve both linear and nonlinear boundary value problems for fourth-order partial differential equations. The numerical results obtained with minimum amount of computation are compared with the exact solution to show the efficiency of the method. The results show that the homotopy perturbation method is of high accuracy and efficient for solving the fourth-order parabolic partial differential equation with variable coefficients. The results show also that the introduced method is a powerful tool for solving the fourth-order parabolic partial differential equations.

scholarly journals Rational Biparameter Homotopy Perturbation Method and Laplace-Padé Coupled Version

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Hector Vazquez-Leal ◽  
Arturo Sarmiento-Reyes ◽  
Yasir Khan ◽  
Uriel Filobello-Nino ◽  
Alejandro Diaz-Sanchez
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Differential Equations ◽  
Approximate Solutions ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Homotopy Perturbation ◽  
Physical Phenomena

The fact that most of the physical phenomena are modelled by nonlinear differential equations underlines the importance of having reliable methods for solving them. This work presents the rational biparameter homotopy perturbation method (RBHPM) as a novel tool with the potential to find approximate solutions for nonlinear differential equations. The method generates the solutions in the form of a quotient of two power series of different homotopy parameters. Besides, in order to improve accuracy, we propose the Laplace-Padé rational biparameter homotopy perturbation method (LPRBHPM), when the solution is expressed as the quotient of two truncated power series. The usage of the method is illustrated with two case studies. On one side, a Ricatti nonlinear differential equation is solved and a comparison with the homotopy perturbation method (HPM) is presented. On the other side, a nonforced Van der Pol Oscillator is analysed and we compare results obtained with RBHPM, LPRBHPM, and HPM in order to conclude that the LPRBHPM and RBHPM methods generate the most accurate approximated solutions.

scholarly journals Convergence of the Generalized Homotopy Perturbation Method for Solving Fractional Order Integro-Differential Equations

2014 ◽  
Vol 11 (4) ◽  
pp. 1637-1648
Author(s):  
Baghdad Science Journal
Keyword(s):  
Theoretical Analysis ◽  
Differential Equations ◽  
Perturbation Method ◽  
Fractional Order ◽  
Infinite Series ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Powerful Method ◽  
Homotopy Perturbation ◽  
Fractional Order Integral

In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.

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