An investigation of Radial Basis Function approximation methods with Application in Dynamic Investment Model

Abstract

The present study is an attempt to investigate some features of Radial Basis Functions (RBFs) approximation methods related to variational problems. Thereby authors applied some properties of RBFs to develop a direct method which reduces constrained variational problem to a static optimization problem. To assess the applicability and effectiveness of the method, some examples are examined. Dynamic investment problem with free endpoint in unbounded domain is solved, accordingly the effectiveness of the proposed method is verified. To improve the accuracy and stability of the method we have used various shape parameter strategies with equally spaced and scattered centers. Finally, two new shape parameter strategies are proposed and then it is shown that the proposed strategies increase the accuracy and stability of the method.