Approximate Solutions to Ordinary Differential Equations Using Least Squares Support Vector Machines


During this paper, a replacement approach based on least squares support vector machines (LS-SVMs) is proposed for solving linear and nonlinear standard differential equations (ODEs). The approximate solution is presented in closed kind by means that of LS-SVMs, whose parameters are adjusted to reduce an appropriate error perform. For the linear and nonlinear cases, these parameters are obtained by solving a system of linear and nonlinear equations, respectively. The method is like minded to solving mildly stiff, nonstiff, and singular ODEs with initial and boundary conditions. Numerical results demonstrate the efficiency of the proposed methodology over existing ways.

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