New perturbation-iteration solutions for Bratu-type equations

Authors:
Yiğit Aksoy;Mehmet Pakdemirli
Affiliations:
Department of Mechanical Engineering, Celal Bayar University, 45140 Muradiye Manisa, Turkey;Department of Mechanical Engineering, Celal Bayar University, 45140 Muradiye Manisa, Turkey
Venue:
Computers & Mathematics with Applications
Year:
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.