Optimized Hybrid Two-Step Four Parameter Block Method for Solving First-Order Ordinary Differential Equations

Using power series and exponential functions as the basis function, this work proposes a two-step, four-parameter optimized hybrid block technique for solving first-order ODEs. This method approximates and generates several continuous schemes. The suggested approach incorporates four free parameters to improve accuracy and flexibility. The method is appropriate for both stiff and non-stiff issues since optimization techniques were used to enhance it and reduce the local truncation error. The optimized continuous method gave rise to the discrete schemes, which were then utilized to concurrently solve initial value problems in block mode. The method's convergence, zero-stability, and consistency are confirmed by a thorough numerical study. The outcomes demonstrate the adaptability and efficiency of the suggested approach in solving a variety of ODE issues, providing a viable instrument for scientific and practical uses.