The approximate solutions to source inverse problem of 1-D convection–diffusion equation by LS-SVM. Issue 5 (4th May 2018)

• Record Type: Journal Article
• Authors: Yu, Jiaju; Li, Fule; Yu, Shuanghe; Wu, Ziku
• Is Part Of: Inverse problems in science and engineering. Volume 26:Issue 5(2018)
• Page Start: 677
• Page End: 690
• Publication Date: 2018-05-04
• Subjects: Least squares support vector machines -- convection–diffusion equation -- source inverse problem -- closed form approximate solution -- quadratic programming; 65N21 -- 80A23 -- 74S99 -- 68T99; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2017.1336553
• Languages: English
• ISSNs: 1741-5977

Abstract

Abstract: This article deals with the determination of the source in 1-D convection–diffusion problem. A method which based on the least squares support vector machines is proposed. The approximate solutions consist of two parts. The first part is a known function that satisfies the initial/boundary conditions. The other part is the combination of Gauss Kernel functions with regression coefficients, which is not affected from the initial/boundary conditions. According to the principle of least squares support vector machines regression, the problem can be transformed into a quadratic programming. The method has been tested on four examples and has yielded accurate results.