Optimal Control of Nonlinear Systems Using the Homotopy Perturbation Method: Infinite Horizon Case

2010 ◽  
Vol 4 (9) ◽  
pp. 114-122 ◽  
Author(s):  
Amin Jajarmi ◽  
Hamidreza Ramezanpour ◽  
Arman sargolzaei ◽  
Pouyan Shafaei
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Infinite Horizon ◽  
Homotopy Perturbation ◽  
Horizon Case

scholarly journals Second Approximate Solution of Duffing Equation with Strong Nonlinearity by Homotopy Perturbation Method

1970 ◽  
Vol 30 ◽  
pp. 59-75
Author(s):  
M Alhaz Uddin ◽  
M Abdus Sattar
Keyword(s):  
Approximate Solution ◽  
Nonlinear Systems ◽  
Perturbation Method ◽  
Differential System ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Second Order ◽  
Strong Nonlinearity ◽  
Analytical Technique ◽  
Homotopy Perturbation

 In this paper, the second order approximate solution of a general second order nonlinear ordinary differential system, modeling damped oscillatory process is considered. The new analytical technique based on the work of He’s homotopy perturbation method is developed to find the periodic solution of a second order ordinary nonlinear differential system with damping effects. Usually the second or higher order approximate solutions are able to give better results than the first order approximate solutions. The results show that the analytical approximate solutions obtained by homotopy perturbation method are uniformly valid on the whole solutions domain and they are suitable not only for strongly nonlinear systems, but also for weakly nonlinear systems. Another advantage of this new analytical technique is that it also works for strongly damped, weakly damped and undamped systems. Figures are provided to show the comparison between the analytical and the numerical solutions. Keywords: Homotopy perturbation method; damped oscillation; nonlinear equation; strong nonlinearity. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 30 (2010) 59-75  DOI: http://dx.doi.org/10.3329/ganit.v30i0.8504

Optimal control homotopy perturbation method for cancer model

2019 ◽  
Vol 12 (03) ◽  
pp. 1950027 ◽  
Author(s):  
Malihe Najafi ◽  
Hadi Basirzadeh
Keyword(s):  
Mathematical Modeling ◽  
Optimal Control ◽  
Perturbation Method ◽  
Cancer Immunotherapy ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Cancer Model ◽  
Homotopy Perturbation

In this paper, we introduced the optimal control homotopy perturbation method (OCHPM) by using the homotopy perturbation method (HPM). Every one, by using of the proposed method, can obtain numerical solutions of mathematical modeling for cancer-immunotherapy. In this paper, in order to prove the preciseness and efficiency of the OCHPM method, we compared the obtained numerical solutions with HPM. The results obtained showed that the OCHPM method is powerful to generate the numerical solutions for some therapeutic models.

Application of Homotopy Perturbation Method for the Generalized Burgers-Fisher Equation

2013 ◽  
Vol 432 ◽  
pp. 173-178
Author(s):  
Jun Yu ◽  
Jian Gang Huang
Keyword(s):  
Nonlinear Systems ◽  
Perturbation Method ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Fisher Equation ◽  
Homotopy Perturbation ◽  
Promising Tool ◽  
The Given

The homotopy perturbation method (HPM) is generalized to solve the generalized Burgers-Fisher equation, and some new analytical solutions for the given system are achieved. Furthermore, the comparison of the result obtained using this method with the exact ones reveals that the HPM is a promising tool for solving nonlinear systems.

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