A rapid algorithm for solution of the equations of multiple equilibrium systems-RAMESES

Area of Science:

• Chemical Engineering
• Computational Chemistry
• Applied Mathematics

Background:

• Solving systems of equilibrium is crucial but often complicated by non-linear relationships.
• Existing numerical methods face challenges with slow convergence, reliability, and structural efficiency.

Purpose of the Study:

• To present a novel algorithm, RAMESES, for efficiently solving systems of equilibrium.
• To address the limitations of previous numerical solution methods.

Main Methods:

• The RAMESES algorithm is formulated using matrix algebra.
• It involves a single matrix inversion for each system of equations.
• The method iteratively solves dependent equilibrium equations.

Main Results:

• RAMESES demonstrates a simple and efficient algorithmic structure.
• The algorithm achieves an exact solution at each iteration.
• It overcomes the slow convergence and unreliability issues of prior methods.

Conclusions:

• RAMESES provides a significant advancement in the numerical solution of non-linear equilibrium systems.
• The algorithm's efficiency and exactness make it a valuable tool for scientific and engineering applications.