Construction of new generating function based on linear barycentric rational interpolation for numerical solution of fractional differential equations

Abstract

In this paper, a new generating function based on linear barycentric rational interpolation is introduced for the numerical solution of fractional differential equations which is designed on fractional linear multistep methods. The consistency of the proposed method is analyzed. considering monotonicity of the coefficients, the stability of the proposed method is presented. Also, the stability regions are determined which show the new scheme improves the stability properties and the accuracy compared with the fractional backward difference formulae. Finally, the extracted numerical results show the effectiveness of the proposed method.