A blended numerical procedure for quadratic riccati differential equations utilizing ramadan group transform and variations of adomian decomposition

To solve the approximate analytic solutions of the quadratic Riccati differential equations, this study introduces a hybrid method that combines an accelerated variant of the Adomian decomposition method (AADM) proposed by I. El-Kalla with the Ramadan Group transform (RGT). This hybrid technique produces accurate and dependable results, outperforming the regular Adomian decomposition method (RADM) and the Newton- Raphson version of Adomian polynomials in terms of accuracy. Three examples are provided here to demonstrate good accuracy and fast convergence when compared to the exact solution and other recent analytical methods using Shifted Chebyshev polynomials, Variation of Parameters Method (VPM), Bezier polynomials, homotopy analysis method (HAM), and Newton – Raphson based modified Laplace Adomian decomposition method.