A novel semi-analytical solution to Jeffery-Hamel equation

Abstract

Abstract A new approach based on the Adomian decomposition and the Fourier transform is introduced. The method suggests a solution for the well-known magneto-hydrodynamic (MHD) Jeffery-Hamel equation. Results of Adomian decomposition method combined with Fourier transform are compared with exact and numerical methods. The FTADM as an exclusive and new method satisfies all boundary and initial conditions over the entire spatial and temporal domains. Moreover, using the FTADM leads to rapid approach of approximate results toward the exact solutions is demonstrated. The second derivative of Jeffery-Hamel solution related to the similar number of items of recursive terms under a vast spatial domain shows the maximum error in the order of 10 − 5 comparing to exact and numerical solutions. The results also imply that the FTADM can be considered as a precise approximation for solving the third-order nonlinear Jeffery-Hamel equations.