The Second-Order Mass-Conservative Characteristic Finite Difference Method for Sobolev Equation with Convection Term (Advances in Applied Mathematics and Mechanics, 2025)
In this work, a new Mass-Conservative Characteristic Finite DifferenceMethod (MCC-FDM) is developed for solving the Sobolev equation. The new methodcombines the method of characteristics with mass-preserving interpolation, which notonly keeps mass balance but also achieves second-order accuracy in both time andspace. Numerical results are presented to confirm the temporal and spatial accuracy