Approximate Solutions to Poisson Equation Using Least Squares Support Vector Machines

  • Ziku Wu
  • Zhenbin Liu
  • Fule Li
  • Jiaju YuEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 120)


This article deals with Poisson Equations with Dirichlet boundary conditions. A new approach based on least squares support vector machines (LS-SVM) is proposed for obtaining their approximate solutions. The approximate solution is presented in closed form by means of LS-SVM, whose parameters are adjusted to minimize an appropriate error function. The approximate solutions consist of two parts. The first part is a known function that satisfies boundary conditions. The other is two terms product. One term is known function which is zero on boundary, another term is unknown which is related to kernel functions. This method has been successfully tested on rectangle and disc domain and has yielded higher accuracy solutions.



This work is supported by the international cooperation for excellent lectures of 2013, Shandong provincial education department, and the NNSF of China (61403233).


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Science and Information CollegeQingdao Agricultural UniversityQingdaoChina
  2. 2.School of Information Science and TechnologyDalian Maritime UniversityDalianChina

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