A computational scheme of exponential integrator for fuzzy electrical boundary layer flow with variable viscosity and thermal conductivity

• Construction of a modified exponential integrator scheme nonstandard numerical scheme is considered for solving PDEs with fuzzy parameters, enhancing the ability to model complex boundary layer flows. • It incorporates fuzzy logic to represent critical parameters such as the Hartmann number, Eckert number, and reaction rate, allowing for the effective handling of uncertainties in fluid properties and external conditions. • A rigorous analysis of the proposed scheme, demonstrating its consistency and stability in the mean square sense, ensures reliability in environmental simulations. • The proposed numerical scheme is highly accurate and attains the predicted order of convergence shown through various examples. • A comparison shows that the proposed scheme consumes almost 50 % less computation time than the existing first and second-order methods regarding accuracy and computational efficiency, particularly across varying time steps. This study aims to d an efficient computational scheme for solving partial differential equations involving fuzzy parameters in boundary layer flow. Specifically, we propose a modified exponential integrator method to handle the challenges of variable viscosity and thermal conductivity in flow over flat and oscillatory sheets. This work aims to enhance accuracy and stability in simulating fluid flows under uncertainty. The proposed explicit scheme operates on two-time levels with compact spatial discretization. The stability and convergence of the proposed scheme are also provided for scalar and system of partial differential equations. Results show that the scheme provides better accuracy than existing first- and second-order methods, especially for specific time steps. Additionally, the method effectively handles fuzzy Hartmann number, Eckert number, and reaction rate parameters, reflecting uncertainties in material properties. The proposed method significantly improves the precision of fluid simulations with complex parameters.