A Nobel Variation of 16th-Order Iterative Scheme for Models in Blood Stream, Chemical Reactor, and Its Dynamics
Аннотация
As science and engineering continue to advance in numerous fields, it has become increasingly difficult to find a fast and accurate solution to non-linear problems in the real world. To resolve these issues, more effective and efficient iterative techniques are required. In this paper, we present a weighted type four-point sixteenth-order iterative scheme of Steffensen–Ostrowski type. Maple 18, a computer algebra system employed to figure out the optimality of the proposed scheme that satisfies the Kung–Traub conjecture and is optimal. The theoretical convergence order of our recently devised scheme was determined to be sixteen. The scheme has applications in numerous fields, such as blood stream dynamics, chemical reactor dynamics, and Kepler’s equation, among others. In addition, numerical testing demonstrates that the developed iterative schemes are more effective than the existing optimal four-point iterative schemes in the domain. Thus, the fourth-step Steffensen–Ostrowski-type weighted family is a more efficient addition to the literature and a superior alternative.