Optima leighth-order multiple root finding iterative methods using bi variate weight function
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Date
2023
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ElsevierB.V
Abstract
Inthiscontribution, anovel eighth-order scheme ispresentedfor solvingnonlinearequations
withmultipleroots.Theproposedschemecomprisesof threestepswiththemodifiedNewton
methodas its first stepfollowedbytwoweightedNewtonsteps involvingoneunivariateand
onebivariatefunctionrespectively.Analysisofconvergenceconfirmsthatthepresentedscheme
obtains optimal computational order of convergence. The efficiencyof presented scheme is
comparednumericallywith recent eighth-ordermethods. Functions like populationgrowth
problem,Newton’sbeamproblem, etc.,havebeenconsideredfornumerical experimentation.
For the comparative study in the complex plane, we employed the concept of basins of
attraction