A cubic interpolation algorithm for solving non-linear equations

Abstract

A new Algorithm - based on cubic interpolation have been developed for solving non-linear algebraic equations. The Algorithm is derived from LaGrange's interpolation polynomial. The method discussed here is faster than the \"Regular Falsi\" which is based on linear interpolation. Since this new method does not involve derivatives, it does not have the problem of non-convergence associated with the Newton - Raphson method, when a small derivative is encountered. The efficiency of the cubic interpolation method was ascertained by practical testing with Leonardo\'s cubic equation and Dranchuk, Purivis and Robinson method for calculating the Gas Compressibility Factor (z) of Natural Gases. The Watfor computer program (based on the new method) that was used to solve the Dranchuk Purivis and Robinson equation is also included in this paper.

Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp. 317-324