Research Article
Some Iterative Methods Free from Derivatives and Their Basins of Attraction for Nonlinear Equations
Algorithm 1
The Mathematica code for finding the asymptotic error constant in Theorem
4.
Clear[“Global’ *” | *Assuming e = x - α and = (f∧(j) (α))/j!, for j = 1, 2, …, 8* | f[e_*e + *e∧2 + *e∧3 + *e∧4 + *e∧5 + *e∧6 + *e∧7 + *e∧8; | *Assuming b = w - α* | fe = f[e]; b = e + β fe; fw = fb; d = fw - feβ fe; | *Assuming u = y - α* | u = e-Seriesfe/d, {e, 0, 8//Simplify; | (*Assuming v = z - α*) | fu fu; v e - fe2dfe - fu - fu2fw//Simplify; | fv fv; fyz fu - fv/u - v; | (*Assuming e Subscriptx, new - α*) | e v - fvfvv - e fyz β dfufe∧2 | +β d β d∧(fu/fw)∧ fvfw fv/fu)∧//FullSimplify |
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