A NOVEL HYBRID ITERATIVE METHOD FOR APPLIED MATHEMATICAL MODELS WITH TIME-EFFICIENCY.

Jamali, Khalid; Solangi, Muhammad Anwar; Qureshi, Sania

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.

MATHEMATICAL models; REAL gases; FLUID dynamics; NONLINEAR equations; NEWTON-Raphson method

Journal of Applied Mathematics & Computational Mechanics, 2022, Vol 21, Issue 3, p19

2299-9965

Academic Journal

10.17512/jamcm.2022.3.02