FINDING ROOTS AND VALUES OF UNKNOWNS THAT PROVIDE THE LEAST OR LARGEST RESOLUTION OF NONLINEAR EQUATIONS

Abstract

This article examines a method for numerically solving nonlinear and transcendental equations in the absence of a priori information about the root localization interval. The authors propose an algorithm for automatically finding the calculation interval followed by root refinement using the dichotomy method, as well as computational procedures for determining the extremum points of the residual function in cases where the equation has no real roots. Based on the developed algorithm, a C++ program was created, the correctness and reliability of which were confirmed by test calculations and comparison with graphical analysis of the residuals.