WSEAS Transactions on Signal Processing
Print ISSN: 1790-5052, E-ISSN: 2224-3488
Volume 11, 2015
An Optimization Method for Numerically Solving Three-Point BVPs of Linear Second-Order ODEs with Variable Coefficients
Authors: ,
Abstract: It is known that most numerical methods for solving differential equations are based on iterative methods or Taylor expansion methods. This paper tries to study a numerical method from a new perspective—optimization method. By means of the idea of kernel ""-SVR, the paper constructs an optimization model for a class of threepoint boundary value problems (BVPs) of linear second-order ordinary differential equations (ODEs) with variable coefficients and proposes a novel numerical method for solving them. The proposed method has a certain versatility and can be used to solve some other kinds of differential equations and integral equations. In order to verify the effectiveness of the proposed method, comparative experiments with six specific linear second-order ODEs are performed. Experimental results show that the proposed method has a good approximation property.
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Keywords: Optimization modeling, numerical method, ordinary differential equation, kernel "-support vector regression, Lagrange function
Pages: 310-316
WSEAS Transactions on Signal Processing, ISSN / E-ISSN: 1790-5052 / 2224-3488, Volume 11, 2015, Art. #37