Modification of Adomianʹs decomposition method to solve equations containing radicals

Adomianʹs decomposition method has been used in obtaining approximate solutions to a wide class of nonlinear deterministic/stochastic operator equations. Adomian, Rach and Sarafyan have investigated the use of the decomposition method for equations involving radicals. But in such equations, when the linear operator is of higher degree, the direct use of Adomian polynomials for the radicals produces computational difficulties while inverting the operator, in particular, if the initial approximation is not a constant. In this paper, we propose a method in which the nonlinear term in the equation involving radicals is first expanded formally in a power series. The power series is then approximated by Padé approximant, thereby replacing the radical term by a ratio of polynomials. The decomposition method of Adomian is now applied to the modified equation without any difficulty as the radical type nonlinearity is now converted into a polynomial type nonlinearity.