فهرست نشریات علمی دسترسی آزاد ایران

The primary objective of this study is to explore numerical techniques for solving intuitionistic fuzzy wave equations, with a focus on applying this approach to bridge suspension cables or strings. Existing intuitionistic fuzzy finite difference methods suffer from the explicit nature of finite differences, leading to conditionally stable solutions. Additionally, most of the uncertainty in the literature is based on the classical fuzzy set. This study extends the explicit fuzzy finite difference scheme to the intuitionistic implicit fuzzy finite difference method for solving intuitionistic fuzzy wave equations. The proposed method uses the second-order finite difference method to approximate the wave equation in implicit form. The initial and boundary conditions of the wave equation are described using intuitionistic triangular fuzzy numbers. The error analysis, consistency, convergence, and stability of the scheme are rigorously analyzed to ensure mathematical reliability. A representative problem from engineering applications, such as analyzing a bridge cable under wind loading, has been solved. To demonstrate the method's practicality, the numerical results are compared with the exact solution. By stability analysis, the method is found to be unconditionally stable. The findings confirm that the proposed approach approximates the solution with high accuracy, making it a significant contribution to numerical methods for solving intuitionistic fuzzy wave equations in real-world applications.