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Figure 3 | Advances in Difference Equations

Figure 3

From: On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation

Figure 3

Figure 3(a), (e), (g), (i), (k), (m), (o) shows basins of attraction of iterative methods Q1, E1–E6 for the nonlinear equation \(f_{3}(x)=x^{6}-ix^{3}+1\) using \(\vert x^{(k+1)}\text{-}x^{(k)} \vert <10^{-3}\). Figure 3(b), (f), (h), (j), (l), (n), (p) shows basins of attraction of iterative methods Q1, E1–E6 using \(\vert f(x^{(k)}) \vert <10^{-3}\). Figure 3(c), (d) shows the basin of attraction for \(\alpha =-0.000001\). In Fig. 3(a)–(p), brightness of color in basins of Q1 shows a lower number of iterations for convergence of iterative method as compared to methods E1–E6.

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