Two Novel Difference Schemes for the One-Dimensional Multi-Term Time Fractional Oldroyd-B Equation

In this paper, two novel difference schemes, which are based on the order reduction technique together with the weighted and shifted Grünwald-Letnikov difference (WSGD) operator, are derived for the one-dimensional multi-term time fractional Oldroyd-B equation. Utilizing the discrete energy method, we proved that the schemes are unconditionally stable and convergent in the maximum norm with the global convergence orders O(τ2-β+h2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\tau ^{2-\beta }+h^{2})$$\end{document} and O(τ2-β+h4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\tau ^{2-\beta }+h^{4})$$\end{document}, respectively. Finally, two numerical examples are carried out to verify the theoretical results, showing that our schemes are efficient indeed and have higher accuracy compared with the existing methods.