Numerical simulation of Emden–Fowler integral equation with Green’s function type kernel by Gegenbauer-wavelet, Taylor-wavelet and Laguerre-wavelet collocation methods

Abstract

In this paper, we consider the Emden–Fowler integral equation with Green’s function type kernel. We propose three computational algorithms based on the Gegenbauer-wavelet, the Taylor-wavelet, and the Laguerre-wavelet to solve such problems. Firstly, we transform the given problems via the collocations technique to the system of algebraic equations, which are then solved by the Newton–Raphson method to get the required numerical solution. We also provide the error bound of the proposed method. To demonstrate the efficiency of the proposed methods, we consider several examples arising in physical models, including real-life problems. The numerical simulations justify the superiority and high performance of the methods, and the obtained results are compared with some other existing schemes. The comparison shows that the proposed method converges faster than other numerical techniques like Haar-wavelets collocation method, advanced Adomian decomposition method, and simplified reproducing kernel method. The numerical tables and graphs show that the accuracy of the proposed method is very high, even for the few collocation points. The L∞ and the L2 errors decrease gradually with an increase in collocation points, and hence, the current method is stable.