New perturbation-iteration solutions for Bratu-type equations
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Date
2010
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Abstract
Perturbation-iteration theory is systematically generated for both linear and nonlinear second-order differential equations and applied to Bratu-type equations. Different perturbation-iteration algorithms depending upon the number of Taylor expansion terms are proposed. Using the iteration formulas derived using different perturbation-iteration algorithms, new solutions of Bratu-type equations are obtained. Solutions constructed using different perturbation-iteration algorithms are contrasted with each other as well as with numerical solutions. It is found that algorithms with more Taylor series expansion terms yield more accurate results. © 2010 Elsevier Ltd. All rights reserved.
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Keywords
Algorithms , Differential equations , Nonlinear equations , Perturbation techniques , Taylor series , Iteration algorithms , Iteration theory , New solutions , Numerical solution , Perturbation method , Second-order differential equation , Taylor expansions , Taylor series expansions , Iterative methods