Numerical solution of higher-order linear and nonlinear ordinary differential equations with orthogonal rational legendre functions

Seyed Rouhollah Alavizadeh, Farid(Mohammad) Maalek Ghaini


In this paper, we describe a method for the solution of linear or nonlinear ordinary differential equations of arbitrary order with initial or boundary conditions (I.B.V.L.N.O.D.E.). In this direction we first investigate some properties of orthogonal rational Legendre functions, and then we give the least square method based on these basis functions for the solution of  I.B.V.L.N.O.D.E.'s.
In this method the solution of an O.D.E. is reduced to a minimization problem, which is then numerically solved via Maple 16. Finally results of this method which are obtained in the form of continuous functions, will be compared with the numerical results in other references.


Ordinary differential equations, Least squares approximation, Legendre polynomials, Orthogonal rational Legendre functions.

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