A new Legendre wavelet operational matrix of derivative and its applications in solving the singular ordinary differential equations

In the present paper, a new Legendre wavelet operational matrix of derivative is presented. Shifted Legendre polynomials and their properties are employed for deriving a general procedure for forming this matrix. The application of the proposed operational matrix for solving initial and boundary value problems is explained. Then the scheme is tested for linear and nonlinear singular examples. The obtained results demonstrate efficiency and capability of the proposed method.