Von neumann stability analysis of a finite volume method for solving a space-fractional cauchy equation

Abstract EN

A new formulation of the finite volume method (FVM) is introduced for solving the space-fractional cauchy equation (SFCE), this method converts the SFCE to the implicit scheme by using the fractional grünwald- letnikov formula.

the von neumann stability analysis shows that the proposed method is conditionally stable.

our examples show the results for different values of fractional order and show the approximated solution is close to the exact solution that revealing the reliability and efficiency of the proposed method.