Comparison of Software Implementations of SLAE Solution Methods in the Problem of Finding the Equilibrium Composition of a Complex Multicomponent Heterogeneous System

The article presents a comparative analysis of the software implementation performance of numerical methods in solving the problem of finding the equilibrium composition of a complex multicomponent heterogeneous system. The task of finding the equilibrium composition of the system is divided into the following subtasks: 1) taking into account constraints (Lagrange method); 2) finding the maximum function of a nonlinear function: 2.1) converting a function into a system of linear equations (Newton Raphson method); 2.2) using numerical methods to solve a system of linear algebraic equations. An analytical review of the literature data has shown that gradient methods have better performance when solving systems of linear algebraic equations. Therefore, the article compared the performance of the software implementation of the entire algorithm using direct (Gauss, LUP decomposition) and iterative methods (conjugate gradient method, biconjugate gradient stabilized method) for solving a system of linear algebraic equations. The calculation speed of the developed program was also compared using dynamically connected libraries Alglib, ILNumerics, MathNet, Accord to solve the SLAE in the problem of finding the equilibrium composition of a thermodynamic system.

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