Abstract A highly recurrent traditional bottleneck in applied mathematics, for which the most popular codes (Mathematica and Matlab) do not offer a solution, is to find all the real solutions of a system of N nonlinear equations in a certain finite domain of the N-dimensional space of variables. We present an algorithm of minimum length and computational weight to solve this problem, resembling a graphical tool of edge detection in an image extended to N dimensions. Once the hypersurfaces (edges) defined by each nonlinear equation have been identified in a single, simultaneous step, the coincidence of the hypersurfaces in the vicinity of all the hyperpoints that constitute the solutions makes the final Newton-Raphson step rapidly convergent to all the solutions with the desired degree of accuracy. As long as N remains smaller than about five, which is often the case for physical systems that depend on fewer than five parameters, this approach demonstrates excellent effectiveness.

Full Text

Published Version
Open DOI Link

Get access to 250M+ research papers

Discover from 40M+ Open access, 3M+ Pre-prints, 9.5M Topics and 32K+ Journals.

Sign Up Now! It's 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