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 \(O(\tau ^{2-\beta }+h^{2})\) $O({\tau }^{2-\beta }+h^2)$ and \(O(\tau ^{2-\beta }+h^{4})\) $O({\tau }^{2-\beta }+h^4)$ , 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.