English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This research was mainly conducted to explore the possibility of formulatingan efficient algorithm to find roots of nonlinear equations without using thederivative of the function. The Weerakoon-Fernando method had been taken as thebase in this project to find a new method without the derivative sinceWeerakoon-Fernando method gives 3rd order convergence. After severalunsuccessful attempts we were able to formulate the Finite DifferenceWeerakoon-Fernando Method (FDWFM) presented here. We noticed that the FDWFMapproaches the root faster than any other existing method in the absence of thederivatives as an example, the popular nonlinear equation solver such as secantmethod (order of convergence is 1.618) in the absence of the derivative. Andthe FDWFM had three function evaluations and secant method had two functionevaluations. By implementing FDWFM on nonlinear equations with complex rootsand also on systems of nonlinear equations, we received very encouragingresults. When applying the FDWFM to systems of nonlinear equations, we resolvedthe involvement of the Jacobian problem by following the procedure in theBroyden's method. The computational order of convergence of the FDWFM was closeto 2.5 for all these cases. This will undoubtedly provide scientists theefficient numerical algorithm, that doesn't need the derivative of the functionto solve nonlinear equations, that they were searching for over centuries.

Finite Difference Weerakoon-Fernando Method to solve nonlinear equations without using derivatives