An Extended Legendre Wavelet Method for Solving Differential Equations with Non-Analytic Solutions

Although spectral methods such as Galerkin and Tau methods do not work well for solving ordinary differential equations in which, at least, one of the coefficient functions or solution function is not analytic [1], but it is shown that the Legendre wavelet Galerkin method is suitable for solving some kind of these problems [4]. In this study we use the extended Legendre wavelet basis and Tau method for solving a wide range of singular boundary value problems. The convergence properties and error analysis of the proposed method are investigated. A comparison between the standard Legendre wavelets and extended Legendre wavelets methods shows the capability of the proposed method.