Two novel difference schemes for the one-dimensional multi-term time fractional Oldroyd-B equation

Abstract 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) and O(τ2−β + h4), respectively. Finally, a numerical example is carried out to verify the theoretical results, showing that our schemes are efficient indeed and have higher accuracy compared with the existed methods.