AUTHORS: Yanmeng Li, Huaijiang Sun, Wenzhu Yan
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ABSTRACT: We know that most of the numerical methods for solving ordinary differential equations (ODEs) are based on iterative techniques or Taylor expansion techniques. In this paper, take three-point boundary value problems (BVPs) of linear second-order ODEs for example, we try to study the numerical solutions of ODEs from a new perspectiveł-machine learning. By means of the idea of least squares support vector regression (LSSVR), we propose a new numerical solving method for three-point BVPs of linear second-order ODEs. From the derivative process of the proposed method, we can see that it has generality and can be used for solving some other kinds of ODEs. In order to verify the effectiveness of the proposed method, we perform a series of comparative experiments with four specific linear second-order ODEs. Experimental results show that the proposed method is a effective menthod.
KEYWORDS: numerical solution; ordinary differential equation; least squares; support vector regression
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