A compact finite difference scheme for the fourth‐order time‐fractional integro‐differential equation with a weakly singular kernel

By Da Xu, Wenlin Qiu, Jing Guo. Numerical Methods for Partial Differential Equations, 2019

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In this paper, a compact finite difference scheme is constructed and investigated for the fourth‐order time‐fractional integro‐differential equation with a weakly singular kernel. In the temporal direction, the Caputo derivative term is treated by means of L1 discrete formula and the Riemann–Liouville fractional integral term is discretized by the second‐order convolution quadrature rule. A fully discrete compact difference scheme is constructed with the space discretization by the fourth‐order compact approximation. The stability and convergence are obtained by the discrete energy method, the Cholesky decomposition and the reduced‐order method. Numerical experiments are presented to verify the theoretical analysis.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/762e31b228e0a00c717995f0ea72ff0b85a49734