Third order derivative free SPH iterative method for solving nonlinear systems

Khalil Maatouk

Applied Mathematics and Computation, 2015, vol. 270, issue C, 557-566

Abstract: The majority of iterative methods to find roots of a function requires the evaluation of derivatives of this function. In this paper, based on the basic principle of the SPH method’s kernel approximation, a kernel approximation was constructed to compute first and second order derivatives through Taylor series expansion. Derivatives in our proposed method were replaced in a Newton-like iterative method to obtain a derivative free SPH iterative method for solving nonlinear systems. To illustrate that the new method has the same order of convergence as the considered iterative method, some numerical examples are presented.

Keywords: Nonlinear system; Newton—Raphson method; Iterative method; Derivative free method; SPH method (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:270:y:2015:i:c:p:557-566

DOI: 10.1016/j.amc.2015.08.083

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