On a reduced cost derivative-free higher-order numerical algorithm for nonlinear systems.

*(English)*Zbl 07241627Summary: A derivative-free iterative method of convergence order five for solving systems of nonlinear equations is presented. The computational efficiency is examined and the comparison between efficiencies of the proposed technique with existing most efficient techniques is performed. It is shown that the new method has less computational cost than the existing counterparts, which implies that the method is computationally more efficient. Numerical problems, including those resulting from discretization of boundary value problem and integral equation, are given to compare the performance of the proposed method with existing methods and to confirm the theoretical results concerning the order of convergence and efficiency. The numerical results, including the elapsed CPU time, confirm the accurate and efficient character of the proposed technique.

##### MSC:

65H10 | Numerical computation of solutions to systems of equations |

41A25 | Rate of convergence, degree of approximation |

65J10 | Numerical solutions to equations with linear operators (do not use 65Fxx) |

##### Keywords:

systems of nonlinear equations; derivative-free methods; fast algorithms; computational efficiency
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\textit{J. R. Sharma} and \textit{D. Kumar}, Comput. Appl. Math. 39, No. 3, Paper No. 202, 19 p. (2020; Zbl 07241627)

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