An analytical method as a preconditioning modeling for systems of linear equations

In this paper, we propose a simple and practical preconditioner based on the homotopy analysis method. Furthermore, using this modeling, we design an efficient algorithm to solve linear systems. Within the computational framework, convection-diffusion equation candidates are investigated and evaluated. Finally, computational comparisons of the standard methods against preconditioned methods based on experiments are presented which illustrate the merits of the simplicity, power, and effectiveness of the proposed algorithm.