The performance evaluation of chaotic maps in estimating the shape parameters of radial basis functions to solve partial differential equations

Purpose: This study aims to investigate the potential of chaotic optimization algorithms in improving performance compared to other optimization methods, focusing on determining the appropriate shape parameter of radial basis functions for solving partial differential equations.Methodology: In this research, a two-stage process is employed where the Kansa method, based on meshless local techniques, is combined with the FCW method. In the first stage, the FCW algorithm is utilized to obtain the optimal shape parameter for radial basis functions, followed by the Kansa method in the second stage to estimate the Root Mean Square (RMS) error for approximate solutions.Findings: Numerical results indicate that approximately 95% of the results obtained from two partial differential equations using PSO and FCW algorithms are similar. These results demonstrate the effectiveness and efficiency of this approach in estimating appropriate shape parameters for solving differential equations.Originality/Value: This study confirms the importance of chaos-based optimization algorithms in solving partial differential equations, which can contribute to future research in this field.