ON TWO-STEP PARALLEL COMPUTER ALGORITHM FOR ALL NONLINEAR EQUATIONS ROOTS WITH ENGINEERING APPLICATIONS - Shams, Mudassir; Kausar, Nasreen; Agarwal, Praveen; Alqahtani, Nouf Abdulrahman; Jeelani, Mdi Begum (WORLD SCIENTIFIC PUBL CO PTE LTD, 2026)
In this paper, we develop an optimal family of two-step single root finding methods with order 4. Furthermore, we modify these numerical schemes to locate all nonlinear real and complex roots at the same time. The order of convergence is demonstrated using convergence analysis to be four for a single root-finding technique and for families of parallel computer methods. Numerical test examples reveal that the developed parallel techniques achieve superior stability and consistency compared to existing approaches.
Keywords: Polynomial; Simultaneous Methods; Computational Time; Fractal; Convergence; Percentage Computational Cost; ITERATIVE METHODS; ZEROS; Mathematics; Science & Technology - Other Topics