TY - JOUR
TI - Solving non-linear equations by fixed point iteration method and its accelerating approach
AU - Chen Chushen
AU - Liao Xiaolian
JN - Thermal Science
PY - 2025
VL - 29
IS - 3
SP - 2031
EP - 2039
PT - Article
AB - Due to the inherent complexity of non-linear equations, finding their  analytical solutions is often challenging, leading to a reliance on  numerical solutions. This article examines key methods for solving these  solutions, beginning with an introduction to the fixed point iteration  method. Through examples, we explore the nuances of this technique in  solving non-linear equations. We then examine Aitken's accelerated method  and Steffensen's iteration approach, and discuss their convergence  properties. By applying these methods to a consistent example, we compare  their effectiveness in achieving similar error accuracy. The analysis shows  that both the Aitken method and the Steffensen method require significant-ly  fewer iterations than the fixed point iteration approach for solving  non-linear equations, with the Steffensen method showing superior  performance over the Aitken method. Finally, we have applied the Steffensen  method to the flash evaporation problem, and the computational results are  highly efficient.