An effective numerical algorithm for coupled systems of Emden-Fowler equations via shifted airfoil functions of the first kind

Abstract

The present paper deals with the designation of a new efficient numerical scheme for numerical solution of a class of coupled systems of Emden-Fowler equations describing several processes in applied sciences and technology. This method combines the shifted version of airfoil functions of the first kind (AFFK) and quasilinearization technique. More specifically, the quasilinearization technique is first applied to the original problem and the shifted AFFK (SAFFK) collocation matrix technique is then constructed for obtaining the solution of resulting family of submodels. We derive the error bound and analyze the convergence properties of the SAFFK. Computational and experimental simulations are carried out to describe the applicability and accuracy of the new technique. To show the benefit of the new approach, the computed numerical outcomes are compared with those results obtained via the Bernoulli and Haar wavelets collocation methods. It is evident from the numerical illustrations that the new developed scheme is superior to the existing available ones. The elapsed CPU time of the proposed method is provided.

Keywords

• collocation points
• convergent analysis
• coupled ODEs
• Emden–Fowler equations
• shifted airfoil functions