(untitled) (Advances in Applied Mathematics and Mechanics, 2025)
In this work, a new Mass-Conservative Characteristic Finite Difference Method (MCC-FDM) is developed for solving the Sobolev equation. The new method combines the method of characteristics with mass-preserving interpolation, which not only keeps mass balance but also achieves second-order accuracy in both time and space. Numerical results are presented to confirm the temporal and spatial accuracy