Numerical Solution of Higher-Order Linear and Nonlinear Ordinary Differential Equations with Orthogonal Rational Legendre Functions

In this paper, we describe a method for the solution oflinear and nonlinear ordinary differential equations ode’s of arbitraryorder with initial or boundary conditions. in this direction we first investigatesome properties of orthogonal rational legendre functions, andthen we give the least square method based on these basis functions forthe solution of such equations. in this method the solution of an ode isreduced to a minimization problem, which is then numerically solved viamaple 16. finally results of this method which are obtained in the formof continuous functions, will be compared with the numerical results inother references.