A new Legendre wavelet operational matrix of derivative and its applications in solving the singular ordinary differential equations (Q658581)

Using the system of Legendre polynomials \({ L_{n}(t)}\) on the interval \([-1,1]\) the authors construct a new system of functions \({\Psi_{n,m}(t)}\) defined on the interval \([0,1]\). The solution of a boundary value problem for a second order differential equation may be expanded in the infinite series by the system \({\Psi_{n,m}(t)}\). The finite sum of this series is considered as the approximate solution of the initial problem. The authors do not compare the results of this method with the these obtained by other methods.