Approximate solutions to ordinary differential equations using least squares support vector machines

Siamak Mehrkanoon, Tillmann Falck, Johan A.K. Suykens

Research output: Contribution to journalArticleAcademicpeer-review

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 languageEnglish
Article number6224185
Pages (from-to)1356-1367
Number of pages12
JournalIEEE Transactions on Neural Networks and Learning Systems
Volume23
Issue number9
DOIs
Publication statusPublished - 2012

Keywords

  • Closed-form approximate solution
  • collocation method
  • least squares support vector machines (LS-SVMs)
  • ordinary differential equations (ODEs)

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