AN OPTIMAL ANALYTICAL METHOD FOR NONLINEAR BOUNDARY VALUE PROBLEMS BASED ON METHOD OF VARIATION OF PARAMETER

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DARZI R.; AGHELI B.

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ISSN: 2588-4824

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2018 | Volume:3 | Issue:12 Page(s): 55-70

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Title

AN OPTIMAL ANALYTICAL METHOD FOR NONLINEAR BOUNDARY VALUE PROBLEMS BASED ON METHOD OF VARIATION OF PARAMETER

Author(s)

DARZI R. | AGHELI B. | Issue Writer Certificate

Keywords

OPTIMAL VARIATION OF PARAMETER METHOD (OVPM)Q1

BOUNDARY VALUE PROBLEMSQ1

STURM- LIOUVILLEQ1

AIRY AND QUANTUM MECHANICAL HARMONIC OSCILLATOR PROBLEMSQ1

Abstract

In this paper, the authors present a modified convergent analytic algorithm for the solution of nonlinear BOUNDARY VALUE PROBLEMS by means of a variable parameter method and briefly, the method is called optimal variable parameter method. This method, based on the embedding of a parameter and an auxiliary operator, provides a computational advantage for the convergence of the approximate solutions of nonlinear differential equations. The developed convergence has been shown and its details are discussed. Additionally, a convenient method is considered for selecting an optimal value of the auxiliary parameter, via minimizing the residual error over the domain of problem. The effectiveness of the method and the accuracy of the proposed algorithm are illustrated by the implementation of physical problems such as Sturm-Liouville problem, Airy equation, and Quantum mechanical harmonic oscillator problem. The numerical results and obtained demonstrate clearly reflect the accuracy of the method and its convergence.

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APA: Copy

DARZI, R., & AGHELI, B.. (2018). AN OPTIMAL ANALYTICAL METHOD FOR NONLINEAR BOUNDARY VALUE PROBLEMS BASED ON METHOD OF VARIATION OF PARAMETER. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 3(12 ), 55-70. SID. https://sid.ir/paper/257366/en

Vancouver: Copy

DARZI R., AGHELI B.. AN OPTIMAL ANALYTICAL METHOD FOR NONLINEAR BOUNDARY VALUE PROBLEMS BASED ON METHOD OF VARIATION OF PARAMETER. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2018;3(12 ):55-70. Available from: https://sid.ir/paper/257366/en

IEEE: Copy

R. DARZI, and B. AGHELI, “AN OPTIMAL ANALYTICAL METHOD FOR NONLINEAR BOUNDARY VALUE PROBLEMS BASED ON METHOD OF VARIATION OF PARAMETER,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 3, no. 12 , pp. 55–70, 2018, [Online]. Available: https://sid.ir/paper/257366/en

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