An Efficient Hybrid Method for the Inverse Fisher Equation via Secretary Bird Optimization

Articles in Press

Document Type : Original Article

Authors

1 School of Mathematics and Computer Science, Damghan University, Damghan 36716-45669, Iran

2 Faculty of Mathematics, Kwantlen Polytechnic University, Surrey, British Columbia, Canada.

Abstract

The estimation of unknown boundary conditions in inverse parabolic partial differential equations (IPDEs), such as the Fisher equation, presents significant challenges due to the ill-posed nature and sensitivity to noise of these problems. Traditional methods often require strong prior assumptions or initial guesses, limiting their general applicability and accuracy. In this paper, we propose a robust hybrid numerical framework that integrates a fully implicit finite difference scheme with the parameter-free Secretary Bird Optimization Algorithm (SBOA) to address inverse Fisher equation problems (IFEPs) without prior knowledge of the unknown boundary function. The SBOA algorithm, inspired by the predator-prey dynamics of secretary birds, is employed to efficiently minimize the discrepancy between numerical solutions and noisy observation data, enabling precise recovery of the unknown boundary condition. Numerical experiments conducted on benchmark IFEPs demonstrate that the proposed method achieves outstanding precision, with relative errors as low as 0.07%, and consistently outperforms nine state-of-the-art metaheuristic algorithms in both accuracy and convergence speed. The algorithm also exhibits strong stability under varying grid sizes and noise levels, with solutions typically obtained within seconds on standard computing hardware. These results affirm the effectiveness and reliability of the SBOA-based framework as a powerful and scalable tool for solving complex inverse problems in computational science and engineering.

Keywords

Main Subjects

Soft Computing Journal

Articles in Press, Accepted Manuscript
Available Online from 02 October 2025

Files

History

  • Receive Date: 13 July 2025
  • Revise Date: 19 August 2025
  • Accept Date: 02 October 2025

Share

How to cite

Statistics