A novel predictive homotopic path tracking algorithm to solve non-linear algebraic equations

In chemical engineering and other areas of mathematics and engineering sciences, systems of non-linear algebraic equations often must be solved, and a problem is that these types of systems often cannot be solved analytically. Homotopic continuation methods are globally convergent and can find several solutions to the analyzed algebraic system and consist of a predictive step followed by a corrective step, which can cause reversion of homotopic path tracking. Therefore, in this work, the use of a homotopy continuation method (HCM) based on a purely predictive methodology is proposed; that is, it only makes use of predictor vectors (without correction vectors) to find the solution to several systems of non-linear algebraic equations with a multiplicity of solutions, employing lower central proccessing unit (CPU) time in comparison with standard homotopic tracking algorithms.