Aksoy Y.Pakdemirli M.2024-07-222024-07-22201008981221http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/18467Perturbation-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.EnglishAlgorithmsDifferential equationsNonlinear equationsPerturbation techniquesTaylor seriesIteration algorithmsIteration theoryNew solutionsNumerical solutionPerturbation methodSecond-order differential equationTaylor expansionsTaylor series expansionsIterative methodsArticle10.1016/j.camwa.2010.01.050