Higher order Emden–Fowler type equations via uniform Haar Wavelet resolution technique

Abstract

A uniform Haar wavelet collocation based method is proposed for finding the numerical results for a class of third order nonlinear (Emden–Fowler type) singular differential equations with initial and boundary conditions. At the point of singularity, the coefficient of the such equation blows up, that causes difficulties in capturing the numerical solutions near the point of singularity. Haar wavelet approach handles this peculiar situation efficiently. The proposed method is employed to reduce the IVPs/BVPs into the system of algebraic equations and the nonlinearity is taken care by Newton–Raphson method. It is demonstrated that, the method is appropriate for both initial as well as boundary conditions as these conditions are taken care automatically. Some numerical examples have been illustrated in order to demonstrate the ease of implementation and applicability of the method. The L2 norm and absolute errors further help to manifest the improvement of the findings with the increase in resolution J. We compare our results with other methods which exists in literature, e.g., variation iteration method (VIM), cubic B-spline method, Differential transformation method (DTM), Iterative decomposition method (IDM) and modified Adomian decomposition method (MADM). The second order convergence and error analysis of the proposed method is established to depict the accuracy and stability of the proposed method.