Document Type : Original Article

Authors

• Javad Alikhani Koupaei ¹
• Mohammad Javad Ebadi ²
• Majid Iran Pour ³

¹ Department of Mathematics, Payame Noor University, Tehran, Iran

² Department of Mathematics, Chabahar Maritime University, Chabahar, Iran

³ Dep. of Computer Science, Payame Noor University: Tehran, Tehran

Abstract

This study aims to compare the performance of the First Carrier Wave Chaos Optimization (FCW) algorithm with other optimization methods to determine the appropriate shape parameter of radial basis functions (RBF) for solving partial differential equations (PDEs). The selection of the FCW method is based on its simplicity and foundational characteristics among chaotic optimization algorithms. To achieve this goal, a two-stage process will be employed, in which the Kanza method, based on non-grid-based local techniques, is combined with the FCW method. In the first stage, the FCW algorithm is used to obtain the optimal shape parameter for the radial basis function, and then in the second step, the Kanza method is employed to estimate the root mean square (RMS) error for the approximate solutions. The numerical results derived from two partial differential equations, employing the PSO and FCW algorithms, reveal an approximate 95% conformity. This signifies the effectiveness and efficiency of this methodology in estimating appropriate shape parameters. It accentuates the pivotal role of chaos-based optimization algorithms as powerful tools in the effective resolution of partial differential equations.

Keywords

• Chaos Optimization Algorithms
• Radial Basis Functions
• Kanza Method
• Partial Differential Equations
• First Carrier Wave Method

Main Subjects

• Mathematical Optimization Models