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Figure 1 | Advances in Difference Equations

Figure 1

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

Figure 1

Figure 1(a), (e), (g), (i), (k), (m), (o) shows basins of attraction of iterative methods Q1, E1–E6 for the nonlinear function \(f_{1}(x)=x^{4}-ix^{2}+1\) using \(\vert x^{(k+1)}\text{-}x^{(k)} \vert <10^{-3}\). Figure 1(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 1(c), (d) shows the basin of attraction for \(\alpha =-0.000001\). In Fig. 1(a)–(p), brightness of color in basins of Q1 shows a lower number of iterations for convergence of iterative methods as compared to methods E1–E6.

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