Abstract
Many of the engineering problems are reduced to solve a nonlinear equation numerically, and as a result, an especial attention to suggest efficient and accurate root solvers is given in literature. Inspired and motivated by the research going on in this area, this paper establishes an efficient general class of root solvers, where per computing step, three evaluations of the function and one evaluation of the first‐order derivative are used to achieve the optimal order of convergence eight. The without‐memory methods from the developed class possess the optimal efficiency index 1.682. In order to show the applicability and validity of the class, some numerical examples are discussed.
Highlights
Numerical solution of nonlinear scalar equations plays a crucial role in many optimization and engineering problems
Many engineering systems can be modeled as neutral delay differential equations NDDEs that involve a time delay in the derivative of the highest order, which are different from retarded delay differential equations RDDEs that do not involve a time delay in the derivative of the highest order
A system, which consists of a mass mounted on a linear spring to which a pendulum is attached via a hinged massless rod, is used to predict the dynamic response of structures to external forces using a set of actuators, and it is modeled as an NDDE if the delay in actuators is taken into consideration 1
Summary
Numerical solution of nonlinear scalar equations plays a crucial role in many optimization and engineering problems. The stability of a delay differential equation can be investigated on the basis of the root location of the characteristic function This simple example shows the importance of numerical root solvers in engineering problems. There are numerical methods, which find one root at a time, such as Newton’s iteration or its variant, and the schemes, which find all the roots at a time, namely, Mathematical Problems in Engineering simultaneous methods, such as Weierstrass method. Soleymani and Mousavi in 7 suggested an iteration without memory scheme including three steps and only four functional evaluations per iteration in what follows:. We should remark that Kung and Traub in 10 conjectured that an iterative scheme without memory by using n evaluations per cycle can arrive at the maximum order of convergence 2n−1.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
