Generalized decomposition method: Applications to nonlinear oscillator and MHD fluid flow past cone/wedge geometries

Abstract

In this article, Adomian decomposition method has been modified and two of the recursive relations for nonlinear oscillator and the nonlinear ordinary differential equation that arise from the boundary layer flow problem has been applied. The MHD, electrically conducted, steady, incompressible, and boundary layer flow past a cone and a wedge problem is modeled and reduced into boundary value problem by applying similarity transformations. Four recursive relations have been constructed with some parameters and some additional functions. The rate of convergence of solutions series is enhanced by imposing the conditions of no secular terms in the solutions series. It is also to be noted that the way of choosing linear operator yields the exact solution of nonlinear boundary value problem in the case of flow past a wedge. Comparisons of the numerical solutions obtained from Matlab solver “bvp4c” with the approximate solutions obtained by the recursive relations of the present method are also presented.