L2-1_σ Scheme on a Graded Mesh for a Multi-term Time-fractional Nonlocal Parabolic Problem
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In this article, we propose numerical scheme for solving a multi-term time-fractional nonlocal parabolic partial differential equation (PDE). The scheme comprises L2-1_σ scheme on a graded mesh in time and Galerkin finite element method (FEM) in space. We present the discrete fractional Grönwall inequality for L2-1_σ scheme in case of multi-term time-fractional derivative, which is a multi-term analogue of <cit.>. We derive a priori bound and error estimate for the fully-discrete solution. The theoretical results are confirmed via numerical experiments. We should note that, though the way of proving the discrete fractional Grönwall inequality is similar to <cit.>, the calculation parts are more complicated in this article.
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