A novel fourth-order iterative method with weight functions for efficiently solving nonlinear equations
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A new class of fourth-order iterative methods is developed for solving nonlinear equations by using the weight functions. Based on the optimality principles of the Kung-Traub conjecture, the proposed method is optimal while maintaining computational efficiency. Furthermore, the effectiveness of these methods has been demonstrated through testing with nonlinear functions and comparison with established schemes, showcasing the favorable qualities of this new approach. Furthermore, the qualification criteria further highlight the effectiveness of the proposed method.
Abstract
A new class of fourth-order iterative methods is developed for solving nonlinear equations by using the weight functions. Based on the optimality principles of the Kung-Traub conjecture, the proposed method is optimal while maintaining computational efficiency. Furthermore, the effectiveness of these methods has been demonstrated through testing with nonlinear functions and comparison with established schemes, showcasing the favorable qualities of this new approach. Furthermore, the qualification criteria further highlight the effectiveness of the proposed method.