A SOLUTION OF RICCATI NONLINEAR DIFFERENTIAL EQUATION USING ENHANCED HOMOTOPY PERTURBATION METHOD (EHPM)

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RANJBAR NOUEI ABOU ALFAZL; HOSSEININIA S.H.; SOLTANI I.; GHASEMI J.

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Paper Information

Journal: INTERNATIONAL JOURNAL OF ENGINEERING Year:2008 | Volume:21 | Issue:1 (TRANSACTIONS B: APPLICATIONS) Page(s): 27-38

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Information Journal Paper

Title

A SOLUTION OF RICCATI NONLINEAR DIFFERENTIAL EQUATION USING ENHANCED HOMOTOPY PERTURBATION METHOD (EHPM)

Author(s)

RANJBAR NOUEI ABOU ALFAZL | HOSSEININIA S.H. | SOLTANI I. | GHASEMI J. | Issue Writer Certificate

Keywords

HOMOTOPY PERTURBATION METHOD

SECULAR TERMS

NONLINEAR DYNAMIC

NONLINEAR DIFFERENTIAL EQUATION

ENHANCED HPM (EHPM)

OPTIMAL CONTROL

Abstract

HOMOTOPY PERTURBATION METHOD is an effective method to find a solution of a NONLINEAR DIFFERENTIAL EQUATION, subjected to a set of boundary condition. In this method a nonlinear and complex differential equation is transformed to series of linear and nonlinear and almost simpler differential equations. These set of equations are then solved secularly. Finally a linear combination of the solutions completes the answer if the convergence is maintained. HPM based solution incorporates some reasonable assumptions. These are inspired from the boundary condition and a separation mechanism. In this paper, the need for stability verification is shown trough some examples. The novel idea is to keep the inherent stability of NONLINEAR DYNAMIC in whole term, even if the selected linear part is not stable. Consequently, HPM is enhanced by a preliminary assumption. The proposed method is applied to Riccati equation as well as some other problems. The simulation result verifies the significance of the method whilst numerical and the exact solutions confirm the achievement.

Cites

NONLINEAR CONTROL OF HEAT TRANSFER DYNAMIC USING HOMOTOPY PERTURBATION METHOD

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APA: Copy

RANJBAR NOUEI, ABOU ALFAZL, HOSSEININIA, S.H., SOLTANI, I., & GHASEMI, J.. (2008). A SOLUTION OF RICCATI NONLINEAR DIFFERENTIAL EQUATION USING ENHANCED HOMOTOPY PERTURBATION METHOD (EHPM). INTERNATIONAL JOURNAL OF ENGINEERING, 21(1 (TRANSACTIONS B: APPLICATIONS)), 27-38. SID. https://sid.ir/paper/355657/en

Vancouver: Copy

RANJBAR NOUEI ABOU ALFAZL, HOSSEININIA S.H., SOLTANI I., GHASEMI J.. A SOLUTION OF RICCATI NONLINEAR DIFFERENTIAL EQUATION USING ENHANCED HOMOTOPY PERTURBATION METHOD (EHPM). INTERNATIONAL JOURNAL OF ENGINEERING[Internet]. 2008;21(1 (TRANSACTIONS B: APPLICATIONS)):27-38. Available from: https://sid.ir/paper/355657/en

IEEE: Copy

ABOU ALFAZL RANJBAR NOUEI, S.H. HOSSEININIA, I. SOLTANI, and J. GHASEMI, “A SOLUTION OF RICCATI NONLINEAR DIFFERENTIAL EQUATION USING ENHANCED HOMOTOPY PERTURBATION METHOD (EHPM),” INTERNATIONAL JOURNAL OF ENGINEERING, vol. 21, no. 1 (TRANSACTIONS B: APPLICATIONS), pp. 27–38, 2008, [Online]. Available: https://sid.ir/paper/355657/en

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