AI Article Synopsis
- The paper introduces a new method using least squares support vector machines (LS-SVMs) to solve both linear and nonlinear ordinary differential equations (ODEs).
- The LS-SVMs provide a closed-form approximate solution by adjusting parameters to minimize an error function, which is achieved by solving corresponding equations.
- The proposed approach is effective for various types of ODEs, including mildly stiff, nonstiff, and singular ones, with numerical results showing it outperforms existing methods.
Article Abstract
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 to solving mildly stiff, nonstiff, and singular ODEs with initial and boundary conditions. Numerical results demonstrate the efficiency of the proposed method over existing methods.
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| http://dx.doi.org/10.1109/TNNLS.2012.2202126 | DOI Listing |
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