Solving calculus of variation problems via multiquadric radial basis function method with optimal shape parameter

Abstract

Abstract In this paper we present callocation method for solving the problems in the calculus of variation (CV) using multiquadratic radial basis functions (MQRBFs). In this method we use the Gauss quadrature rule for approximating the integral in CV problems. The effects of the shape parameter of MQRBFs on the convergence of the method have been discussed. Illustrative examples are included to evaluate the capability of the proposed method.