Abstract
We propose a class of composite Newton–Jarratt iterative methods with increasing convergence order for approximating the solutions of systems of nonlinear equations. Novelty of the methods is that in each step the order of convergence is increased by an amount of two at the cost of only one additional function evaluation. Moreover, the use of only a single inverse operator in each iteration makes the algorithms computationally more efficient. Theoretical results regarding convergence and computational efficiency are verified through numerical problems, including those that arise from boundary value problems. By way of comparison, it is shown that the novel methods are more efficient than their existing counterparts, especially when applied to solve the large systems of equations.
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Sharma, J.R., Kumar, S. A class of accurate Newton–Jarratt-like methods with applications to nonlinear models. Comp. Appl. Math. 41, 46 (2022). https://doi.org/10.1007/s40314-021-01739-5
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DOI: https://doi.org/10.1007/s40314-021-01739-5