New LS-SVM approximate solutions to ordinary differential equations

In this paper a new method is proposed to solve morder linear and one order nonlinear ordinary differential equations (ODEs) based on Least Squares Support Vector Machines (LS-SVMs). At first, an appropriate transition is made from the ODEs to an optimization problem, after which the algorithm solves the optimization problem in the LS-SVM framework. Finally a high-accuracy differentiable approximate solution with simple and fixed structure is presented in closed form. Numerical results demonstrate the efficiency of the proposed method for solving non-stiff and singular ordinary differential equations with initial or boundary conditions.