Construction of a Parametric Derivative-Free Iterative Method With Memory for Dynamic System Analysis

WANG Ting; TANG Shuo

doi:10.21656/1000-0887.370350

Volume 38 Issue 12

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WANG Ting, TANG Shuo. Construction of a Parametric Derivative-Free Iterative Method With Memory for Dynamic System Analysis[J]. Applied Mathematics and Mechanics, 2017, 38(12): 1342-1358. doi: 10.21656/1000-0887.370350

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Construction of a Parametric Derivative-Free Iterative Method With Memory for Dynamic System Analysis

doi: 10.21656/1000-0887.370350

School of Mathematics, Hefei University of Technology, Hefei 230009, P.R.China

Funds: The National Natural Science Foundation of China(61272024)

Received Date: 2016-11-14
Rev Recd Date: 2017-10-16
Publish Date: 2017-12-15

Abstract

Abstract

According to the usual practice that 2-step iterative methods with derivative are transformed into derivative-free schemes, a more general 2-step derivative-free iterative method was proposed. For this method the optimal order of convergence was ensured by the weight value. By means of the self-accelerating parameter and the Newton interpolation polynomial, the 2-parameter and 3-parameter iterative schemes with memory were obtained. Some of the existing 2- and 3-parameter iterative methods with memory were compared with the proposed method. The attraction domains of several schemes were presented, and the performances of several iterative schemes were compared.
- non-linear equation,
- order of convergence,
- method with or without memory,
- derivative-free,
- self-accelerating parameter

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References(17)

References

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