Nonuniform difference schemes for multi-term and distributed-order fractional parabolic equations with fractional Laplacian

Abstract

In this paper, the multi-term temporal fractional order and temporal distributed-order parabolic equations with fractional Laplacian are numerically investigated. Several unconditional stable difference schemes based on non-uniform meshes for solving these differential equations are provided. We find that the constructed nonuniform difference schemes are convergent and it has been shown that the temporal convergence rate is faster and more accurate compared to the uniform difference schemes in case of nonsmooth solutions with respect to time. Some numerical examples are given to verify the theoretical findings.