In this paper a new approach based on Least Squares Support Vector Machines (LS-SVMs) is proposed for solving linear and nonlinear ordinary differential equations (ODEs). The approximate solution is presented in closed form by means of LS-SVMs, whose parameters are adjusted to minimize an appropriate error function. For the linear and nonlinear cases, these parameters are obtained by solving a system of linear and nonlinear equations respectively. The method is well suited for solving mildly

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... ff, nonstiff and singular ordinary differential equations with initial and boundary conditions. Numerical results demonstrate the efficiency of the proposed method over existing methods. Index Terms-Least squares support vector machines, ordinary differential equations, closed form approximate solution, Collocation method.