An improved optimal homotopy analysis algorithm for nonlinear differential equations

Abstract This paper presents an improved optimal homotopy analysis algorithm to deal with nonlinear first-order differential equations. We discuss the optimal selection of the auxiliary linear operator in the application of the homotopy analysis method that will accelerate the convergence of series solutions. Then, a powerful algorithm, that employed the optimal auxiliary linear operator, of the homotopy analysis method is presented to facilitate the calculations. Numerical illustrations are examined to show the efficiency and the pertinent features of the proposed algorithm. This algorithm could lead to a promising approach for many nonlinear problems in applied sciences.