A second-order finite difference method for the multi-term fourth-order integral–differential equations on graded meshes

A second-order difference method on graded meshes is proposed for the multi-term fourth-order evolution equation (FOEE). We handle the Riemann–Liouvile fractional integral by the product integration rule on the graded meshes and the spatial derivatives by the second order central difference formula. Stability and convergence of the L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2$$\end{document}-norm is provided. Finally, some numerical examples are given to verify the theoretical analysis and the validity of the proposed method.