Analytical and numerical solutions of a two‐dimensional multi‐term time‐fractional Oldroyd‐B model |
| |
Authors: | Jinghua Zhang Fawang Liu Vo V Anh |
| |
Abstract: | In this paper, we consider a two‐dimensional multi‐term time‐fractional Oldroyd‐B equation on a rectangular domain. Its analytical solution is obtained by the method of separation of variables. We employ the finite difference method with a discretization of the Caputo time‐fractional derivative to obtain an implicit difference approximation for the equation. Stability and convergence of the approximation scheme are established in the L∞ ‐norm. Two examples are given to illustrate the theoretical analysis and analytical solution. The results indicate that the present numerical method is effective for this general two‐dimensional multi‐term time‐fractional Oldroyd‐B model. |
| |
Keywords: | Caputo fractional derivative finite difference method fractional Oldroyd‐B model multi‐term time‐fractional derivative |
|