Approximate Solutions to Poisson Equation Using Least Squares Support Vector Machines

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.