An Improved RBF Method for Solving Variational Problems Arising from Dynamic Economic Models

This paper developes a direct method for solving variational problems via a set of Radial Basis Functions (RBFs) . Operational matrices of differentiation, the product of two RBF vectors and some other formulas are derived and are utilized to propose a method which essentially reduces a variational problem to the linear system of algebraic equations. National saving problem is considered and solved by proposed method which experimentally illustrates effectiveness and applicability of the method. Some experiments are conducted in order to compare the accuracy and stability of several shape parameter strategies in these type of problems. Finally a novel shape parameter strategy is proposed which promotes accuracy and stability of the method.