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Abstract
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Inthispaper,wesuggestasixthorderconvergencethree-stepmethodtosolvesystemofnonlinearequations.Everyiterationofthemethodrequirestwofunctionevaluations,twofirstFréchetderivativeevaluationsandtwomatrixinversions.Hence,theefficiencyindexis61/(2n+6n2+43n3),whichisbetterthanthatofothersixthordermethods.Theadvantagesofthemethodlieinthefeaturethatthistechniquenotonlyachievesanapproximatesolutionwithhighaccuracy,butalsoimprovesthecalculationspeed.Also,underseveralmildconditionstheconvergenceanalysisoftheproposedmethodisprovided.Anefficienterrorestimationispresentedfortheapproximatesolution.Numericalexamplesareincludedtodemonstratethevalidityandapplicabilityofthemethodandthecomparisonsaremadewiththeexistingresults.
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