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On a reduced cost derivative-free higher-order numerical algorithm for nonlinear systems. (English) Zbl 07241627
Summary: 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.
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)
Mathematica; MPFR
Full Text: DOI
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