Learning solutions to a Cauchy problem for the modified Helmholtz equations using LS-SVM. Issue 2 (15th September 2020) - Wu, Ziku; Han, Xiaoming; Li, GuoFeng
Abstract : Purpose: The purpose of this paper is to develop a mesh-free algorithm based on the least square support vector machines method for numerical simulation of the modified Helmholtz equations. Design/methodology/approach: The proposed method deals with a Cauchy problem for the modified Helmholtz equations. The algorithm converts the problem into a quadratic programming. It can be divided into three steps. First, some training points are allocated. Then, an approximate function is constructed. Finally, the shape parameters are estimated. Findings: The proposed method's stability is discussed. Numerical experiments are conducted to check the efficiency of the algorithm. The proposed method is found to feasible for the ill-posed problems of the modified Helmholtz equations. Originality/value: The originality lies in that the proposed method is applied to solve the modified Helmholtz equations for the first time, and the expected results are obtained.