RESOLVING NONLINEAR PHYSICS PROBLEMS WITH AN EFFICIENT SEVENTH ORDER ITERATIVE APPROACH
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Date
2024
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South East Asian J. of Mathematics and Mathematical Sciences Vol. 20, No. 2 (2024), pp. 269-282
Abstract
Our research introduces a novel seventh-order iterative method specifically designed to address nonlinear equations having multiple roots. Inspired by
the pioneering work of Sharma et al. (2019), our approach represents a significant advancement in computational techniques for solving complex mathematical
problems. Through rigorous convergence analysis, we establish that our proposed
method achieves seventh-order convergence. To evaluate its efficacy, we conduct extensive numerical experiments utilizing a range of nonlinear equations encountered
in applied physics domains, including Planck’s Law, electron trajectory problems,
and Newton’s beam designing problem. Our findings reveal that the suggested
method consistently outperforms other existing techniques of similar nature available in the literature. Notably, our method demonstrates exceptional convergence
behavior even in challenging scenarios involving multiple roots, indicating its suitability for solving complex problems encountered in applied physics and related
fields. This superiority is evidenced by its ability to efficiently converge to solutions even in scenarios involving multiple roots. The practical implications of our
research extend to various fields reliant on nonlinear equation.