NUMERICAL ANALYSIS OF LUCAS POLYNOMIALS INNOVATIVE TECHNIQUE WITHIN THE GALERKIN STRATEGY FOR SOLVING FUZZY-TYPE DIFFERENTIAL MODELS WITH AN APPLICATION IN THE ELECTRICAL CIRCUIT ENGINEERING FIELD

Abstract

Modeling uncertain dynamical models with fuzzy differential approaches is important in different practical fields. This investigation presents an innovative technique for solving uncertain models using Lucas polynomials within the Galerkin strategy. We establish essential definitions and preliminary results of the Lucas polynomials and derive the iterative technique for numerically approximating solutions using the Galerkin strategy. The fuzzy differential models are transformed into algebraic transcendental equations, and the numerically estimated solutions are derived by solving the resultant system. To modify and adjust the technique’s efficacy, we carry out and validate the convergence and error estimation requirements. The utilized numerical procedure brings five great benefits: it recognizes solutions globally, shows off high levels of accuracy and efficiency, excels in solving nonlinearity terms, is still unaffected by discretization errors and computational round-off matters, and uses a small number of iterative steps. To demonstrate the importance of fuzzy-type models, we go into great depth about an electrical engineering application and highlight the significance of its uncertainty modeling. By eliminating the importance of wide computational resources, the approach used displays superior performance compared to existing methodologies. Several comparison tables with the Hilpert kernel strategy are tabulated to test the accuracy of the Lucas Galerkin approach. The expected results have the potential to have a considerable influence on scientific and engineering sectors where uncertain and dependable mathematical modeling is critical.