Chih-Wen Chang , Sania Qureshi , Ioannis K. Argyros , Francisco I. Chicharro , Amanullah Soomro
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A modified two-step optimal iterative method for solving nonlinear models in one and higher dimensions
Iterative methods are essential tools in computational science, particularly for addressing nonlinear models. This study introduces a novel two-step optimal iterative root-finding method designed to solve nonlinear equations and systems of nonlinear equations. The proposed method exhibits the optimal convergence, adhering to the Kung-Traub conjecture, and necessitates only three function evaluations per iteration to achieve a fourth-order optimal iterative process. The development of this method involves the amalgamation of two well-established third-order iterative techniques. Comprehensive local and semilocal convergence analyses are conducted, accompanied by a stability investigation of the proposed approach. This method marks a substantial enhancement over existing optimal iterative methods, as evidenced by its performance in various nonlinear models. Extensive testing demonstrates that the proposed method consistently yields accurate and efficient results, surpassing existing algorithms in both speed and accuracy. Numerical simulations, including real-world models such as boundary value problems and integral equations, indicate that the proposed optimal method outperforms several contemporary optimal iterative techniques.
期刊介绍:
The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles.
Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO.
Topics covered by the journal include mathematical tools in:
•The foundations of systems modelling
•Numerical analysis and the development of algorithms for simulation
They also include considerations about computer hardware for simulation and about special software and compilers.
The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research.
The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.