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.
Original language | English |
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Pages (from-to) | 1356-1367 |
Number of pages | 12 |
Journal | IEEE Transactions on Neural Networks and Learning Systems |
Volume | 23 |
Issue number | 9 |
DOIs | |
Publication status | Published - Sept 2012 |
Externally published | Yes |
Keywords
- Closed-form approximate solution
- collocation method
- least squares support vector machines (LS-SVMs)
- ordinary differential equations (ODEs)
- BOUNDARY-VALUE-PROBLEMS
- NEURAL-NETWORK METHOD
- SOLVING ORDINARY
- ALGORITHM