Solving ordinary differential equations by LS-SVM. (English) Zbl 07914324
Rad, Jamal Amani (ed.) et al., Learning with fractional orthogonal kernel classifiers in support vector machines. Theory, algorithms and applications. Singapore: Springer. Ind. Appl. Math., 147-170 (2023).
Summary: In this chapter, we propose a machine learning method for solving a class of linear and nonlinear ordinary differential equations (ODEs) which is based on the least squares-support vector machines (LS-SVM) with collocation procedure. One of the most important and practical models in this category is Lane-Emden type equations. By using LS-SVM for solving these types of equations, the solution is expanded based on rational Legendre functions and the LS-SVM formulation is presented. Based on this, the linear problems are solved in dual form and a system of linear algebraic equations is concluded. Finally, by presenting some numerical examples, the results of the current method are compared with other methods. The comparison shows that the proposed method is fast and highly accurate with exponential convergence.
For the entire collection see [Zbl 1530.68039].
For the entire collection see [Zbl 1530.68039].
MSC:
| 68T05 | Learning and adaptive systems in artificial intelligence |
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 33C99 | Hypergeometric functions |
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