Spectral metaheuristic solver for boundary value problems
Year: 2024
Type: article
Abstract: This study presents an advanced variant of spectral method in combination with a metaheuristic algorithm to solve boundary value problems. The proposed methodology follows a systematic process that starts by obtaining an approximate solution formula using the initial step of spectral method, where Chebyshev polynomials have been utilized. Then, calculate a global residue function by the root mean square analysis. After, implement flower pollination algorithm in aim to minimize the residual calculated and to find the optimum solution for that. Finally, substitute the results in the approximation formula to get the spectral metaheuristic solver's solution. Numerical calculations have been done using spectral method then, spectral metaheuristic solver. In which, different types of boundary value problems have been solved, a homogeneous linear boundary value problem, a non-homogeneous linear boundary value problem and a non-linear boundary value problem as examples. A comparison between the approximations given by the two methods and the analytical solution have been done, and the results obtained have been illustrated in curves, and in a table that contains the errors. the pictures and the table demonstrate the efficiency and the superiority of the suggested approach in solving differential equations specifically for boundary value problems. By showcasing the capability of incorporating metaheuristic algorithms into a classical numerical method to improve and speed up solutions, this study makes a substantial contribution to the advancement of computational methods for solving differential equations.
Authors: Fatiha Ghedjemis, Naceur Khelil
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404399943