Attracting periodic cycles for an optimal fourth-order nonlinear solver. (English) Zbl 1237.65072

Summary: We consider an optimal fourth-order method for solving nonlinear equations and construct polynomials such that the rational map arising from the method applied to these polynomials has an attracting periodic orbit of any prescribed period.


65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
Full Text: DOI


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