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<p>This paper presents a new time-space two-grid (TSTG) method for the two-dimensional nonlinear nonlocal mobile/immobile transport model. The presence of interpolation in both the spatial and temporal directions from coarse grids to fine grids allows investigation into the properties of the high-order mapping operator, crucial for analyzing of the TSTG difference method. The existence and uniqueness of the solution for the proposed TSTG difference scheme are demonstrated, a rarity in prior research. Unconditional stability and convergence of the TSTG scheme are proven, and the optimal error estimate in the discrete <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-norm is obtained. Compared with other two-grid (TG) methods in previous work, the TSTG method features more flexible and simpler mesh selection. It is, to some extent, more adaptable to varying scales of data. We compare the TSTG difference scheme, the general finite difference (GFD) scheme, and the time two-grid (TTG) difference scheme from Qiu, Xu, Guo, Zhou.: A time two-grid algorithm based on finite difference method for the two-dimensional nonlinear time-fractional mobile/immobile transport model. Numerical Algorithms <b>85</b>(1), 39–58 (2020) by solving the nonlinear problem through numerical examples. Numerical results confirm the theoretical findings and demonstrate the superior computational efficiency of the new TSTG technique.</p>

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Analysis of a New Time-Space Two-Grid Method for the Two-Dimensional Nonlinear Nonlocal Mobile/Immobile Transport Model

  • 期刊论文

  • 发表日期：

    2026年5月11日

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  • Xuehua Yang,
  • Yang Shi,
  • Haixiang Zhang,
  • Zhimin Zhang

摘要

This paper presents a new time-space two-grid (TSTG) method for the two-dimensional nonlinear nonlocal mobile/immobile transport model. The presence of interpolation in both the spatial and temporal directions from coarse grids to fine grids allows investigation into the properties of the high-order mapping operator, crucial for analyzing of the TSTG difference method. The existence and uniqueness of the solution for the proposed TSTG difference scheme are demonstrated, a rarity in prior research. Unconditional stability and convergence of the TSTG scheme are proven, and the optimal error estimate in the discrete \(L^2\) L 2 -norm is obtained. Compared with other two-grid (TG) methods in previous work, the TSTG method features more flexible and simpler mesh selection. It is, to some extent, more adaptable to varying scales of data. We compare the TSTG difference scheme, the general finite difference (GFD) scheme, and the time two-grid (TTG) difference scheme from Qiu, Xu, Guo, Zhou.: A time two-grid algorithm based on finite difference method for the two-dimensional nonlinear time-fractional mobile/immobile transport model. Numerical Algorithms 85(1), 39–58 (2020) by solving the nonlinear problem through numerical examples. Numerical results confirm the theoretical findings and demonstrate the superior computational efficiency of the new TSTG technique.