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Modified Jarratt method with sixth-order convergence. (English) Zbl 1184.65054

Summary: We present a variant of Jarratt method with order of convergence six for solving non-linear equations [cf. J. Kou and Y. Li, Appl. Math. Comput. 189, No. 2, 1816–1821 (2007; Zbl 1122.65338)]. Per iteration the method requires two evaluations of the function and two of its first derivatives. The new multistep iteration scheme, based on the new method, is developed and numerical tests verifying the theory are also given.

MSC:

65H05 Numerical computation of solutions to single equations

Citations:

Zbl 1122.65338
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References:

[1] Ostrowski, A. M., Solutions of Equations and System of Equations (1960), Academic Press: Academic Press New York · Zbl 0115.11201
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