Block-pulse functions method for solving three-dimensional fractional Poisson type equations with Neumann boundary conditions

Abstract

Abstract In this paper, a numerical scheme based on the three-dimensional block-pulse functions is proposed to solve the three-dimensional fractional Poisson type equations with Neumann boundary conditions. The differential operational matrices of fractional order of the three-dimensional block-pulse functions are derived from one-dimensional block-pulse functions, which are used to reduce the original problem to solve a system of linear algebra equations. In addition, the convergence analysis of the proposed method is deeply investigated. Lastly, several numerical examples are presented and the numerical results obtained show that our method is effective and feasible.

Keywords

• Three-dimensional block-pulse functions
• Operational matrices
• Convergence analysis
• The approximate solutions
• Fractional order