Stability Analysis of an L2 Type Numerical Scheme for the Steklov Nonlocal Boundary Value Problems in Time-Fractional Diffusion Equations

Abstract

This research examines the time-fractional diffusion equation regarding variable coefficients, considering second-kind Steklov nonlocal boundary conditions that include three real parameters. The Caputo’s definition of the time-fractional derivative is used. A difference scheme of temporal order 3-δ, where δ represents the order of the time-fractional derivative, is developed using an L2 type approach. In the spatial direction a second-order approximation is employed. The stability and convergence of the proposed difference scheme are analyzed through the method of energy inequalities, which results in the establishment of the a priori estimates for the scheme.