Newton-Raphson based modified Laplace Adomian decomposition method for solving quadratic Riccati differential equations

Abstract

Numerical Laplace transform method is applied to approximate the solution of nonlinear (quadratic) Riccati differential equations mingled with Adomian decomposition method. A new technique is proposed in this work by reintroducing the unknown function in Adomian polynomial with that of well known Newton-Raphson formula. The solutions obtained by the iterative algorithm are exhibited in an infinite series. The simplicity and efficacy of method is manifested with some examples in which comparisons are made among the exact solutions, ADM (Adomian decomposition method), HPM (Homotopy perturbation method), Taylor series method and the proposed scheme.