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New perturbation-iteration solutions for Bratu-type equations. (English) Zbl 1193.34015
Summary: 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.
MSC:
34A45Theoretical approximation of solutions of ODE
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