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

Although spectral methods such as galerkin and tau methodsdo 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 issuitable for solving some kind of these problems [4]. in this study we usethe extended legendre wavelet basis and tau method for solving a widerange of singular boundary value problems. the convergence propertiesand error analysis of the proposed method are investigated. a comparisonbetween the standard legendre wavelets and extended legendrewavelets methods shows the capability of the proposed method.