A novel hybrid iterative method for applied mathematical models with time-efficiency

• Autorzy: Jamali Khalid , Solangi Muhammad Anwar , Qureshi Sania

Identyfikatory

DOI

10.17512/jamcm.2022.3.02

• Języki publikacji: EN

Abstrakty

EN

Non-linear phenomena appear in many fields of engineering and science. Research on numerical methods is continually extending with the improvement of the latest computing tools. In today’s computational field, one requires maximum achievement in a minimum amount of time. Therefore, there is a need to modify the Newton-type method to achieve higher-order convergence to solve non-linear equations. While the modified methods are expected to be higher-order convergent, the minor computational information and the maximum time efficiency are also important factors. We propose a three-step hybrid iterative method having a non-linear nature. Per iteration, the method requires three function evaluations and three first-order derivatives. The method is theoretically proven to be tenth-order convergent. The mathematical results of the proposed strategy to solve models from fluid dynamics, electric field, and real gases demonstrated better performance. In light of error analysis, computational productivity, and CPU times, the proposed method’s performance is compared to the famous Newton and a recently proposed tenth-order method.

Słowa kluczowe

EN

nonlinear equation; computational order; efficiency index; convergence order; Newton’s method

PL

równanie nieliniowe; porządek obliczeniowy; wskaźnik efektywności; metoda Newtona

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2022
• Tom: Vol. 21, nr 3
• Strony: 19--29
• Opis fizyczny: Bibliogr. 25 poz., tab.

Twórcy

autor

Jamali Khalid

• Department of Basic Sciences and Related Studies, Mehran University of Engineering & Technology Jamshoro, Pakistan

autor

Solangi Muhammad Anwar

• Department of Basic Sciences and Related Studies, Mehran University of Engineering & Technology Jamshoro, Pakistan

autor

Qureshi Sania

• Department of Basic Sciences and Related Studies, Mehran University of Engineering & Technology Jamshoro, Pakistan

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).