The Second-Order Mass-Conservative Characteristic Finite Difference Method for Sobolev Equation with Convection Term

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Abstract

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

Keywords:

Mass-conservative finite difference second-order accuracy in time Sobolev equation

Author Biographies

  • Kai Fu

    School of Mathematical Sciences, Ocean University of China, Qingdao, Shandong 266100, China

  • Zhaohui Liu

    College of Science, China University of Petroleum, Qingdao, Shandong 266580, China

  • Jiansong Zhang

    College of Science, China University of Petroleum, Qingdao, Shandong 266580, China

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DOI

10.4208/aamm.OA-2024-0154

How to Cite

[1]
2025. The Second-Order Mass-Conservative Characteristic Finite Difference Method for Sobolev Equation with Convection Term. Advances in Applied Mathematics and Mechanics. 17, 7 (Nov. 2025). DOI:https://doi.org/10.4208/aamm.OA-2024-0154.