Comparative study of eighth-order methods for finding simple roots of nonlinear equations
MetadataShow full item record
Recently, there were many papers discussing the basins of attraction of various methods and ideas how to choose the parameters appearing in families of methods and weight functions used. Here, we collected many of the eighth-order schemes scattered in the literature and presented a quantitative comparison. We have used the average number of function evaluations per point, the CPU time, and the number of black points to compare the methods. Based on seven examples, we found that the best method based on the three criteria is SA8 due to Sharma and Arora.
Showing items related by title, author, creator and subject.
Kelly, J.F.; Giraldo, Francis X.; Constantinescu, E.M. (2013);We derive an implicit-explicit (IMEX) formalism for the three-dimensional Euler equations that allow a unified representation of various nonhydrostatic flow regimes, including cloud-resolving and mesoscale (flow in a 3D ...
Arnason, G.; Haltiner, G.J.; Frawley, M.J. (1962-05);Two iterative methods are described for obtaining horizontal winds from the pressure-height field by means of higher-order geostrophic approximations for the purpose of improving upon the geostrophic wind. The convergence ...
Exponential leap-forward gradient scheme for determining the isothermal layer depth from profile data Chu, P.C.; Fan, C.W. (Springer, 2017);Two distinct layers usually exist in the upper ocean. The rst has a near-zero vertical gradient in temperature (or density) from the surface and is called the iso-thermal layer (or mixed layer). Beneath that is a layer ...