New LS-SVM approximate solutions to ordinary differential equations

Author

Guoshan Zhang ; Yiming Wang ; Shiwei Wang ; Wanquan Liu

Author_Institution

Sch. of Electr. Eng. & Autom., Tianjin Univ., Tianjin, China

fYear

2013

Firstpage

7851

Lastpage

7856

Abstract

In this paper a new method is proposed to solve morder linear and one order nonlinear ordinary differential equations (ODEs) based on Least Squares Support Vector Machines (LS-SVMs). At first, an appropriate transition is made from the ODEs to an optimization problem, after which the algorithm solves the optimization problem in the LS-SVM framework. Finally a high-accuracy differentiable approximate solution with simple and fixed structure is presented in closed form. Numerical results demonstrate the efficiency of the proposed method for solving non-stiff and singular ordinary differential equations with initial or boundary conditions.

Keywords

differential equations; least squares approximations; mathematics computing; optimisation; support vector machines; LS-SVM approximate solutions; ODE; boundary conditions; differentiable approximate solution; initial conditions; least square support vector machines; nonstiff ordinary differential equations; one order nonlinear ordinary differential equations; optimization problem; singular ordinary differential equations; Differential equations; Educational institutions; Electrical engineering; Electronic mail; Least squares approximations; Optimization; Support vector machines; Least squares support vector machines; approximate solution; optimization problem; ordinary differential equations;

fLanguage

English

Publisher

ieee

Conference_Titel

Control Conference (CCC), 2013 32nd Chinese

Conference_Location

Xi´an

Type

conf

Filename

6640822