The compact difference scheme for the fourth‐order nonlocal evolution equation with a weakly singular kernel

Abstract

In this paper, we main discuss an efficient numerical algorithm for the fourth‐order nonlocal evolution equation with a weakly singular kernel. The second‐order fractional convolution quadrature rule and L1 method are proposed to approximate the Riemann–Liouville (R‐L) fractional integral term and the temporal Caputo derivative, respectively. In order to obtain a fully discrete method, the compact difference scheme is used to discretize the second‐order and fourth‐order spatial derivative. Further, two new approaches are adopted for stability analysis, and then the optimal error estimates in the discrete ‐norm and ‐norm are obtained. At last, we give three test problems to illustrate the validity of the methods.