Optimizing Solution Strategies for Falkner-Skan Equation: LSTM, FCNN, and Runge-Kutta Performance Analysis

The Falkner-Skan equation governs boundary layer flows in fluid mechanics and aerodynamics. This study compares computational techniques for solving it, analyzing efficacy, performance, and accuracy. Describing flow dynamics near solid surfaces, the equation is crucial for understanding aerodynamic behaviors. Long Short-Term Memory (LSTM) networks, Fully Connected Neural Networks (FCNNs), and the traditional Runge-Kutta method are applied. Training these models with varying epochs evaluates their efficiency and accuracy. Results show LSTM with 100 epochs as the most efficient, followed closely by FCNN with similar epochs. However, the Runge-Kutta method, though accurate, is notably slower. The study reveals trade-offs between neural network-based and traditional numerical approaches in solving the Falkner-Skan equation, with LSTM demonstrating the best computational performance, followed by FCNN, while RungeKutta emphasizes accuracy despite longer computational times.