A new Legendre wavelet operational matrix of derivative and its applications in solving the singular ordinary differential equations. (English) Zbl 1237.65079

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.


65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65T60 Numerical methods for wavelets
34B15 Nonlinear boundary value problems for ordinary differential equations
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