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The conservative characteristic difference method and analysis for solving two-sided space-fractional advection-diffusion equations

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Abstract

In this paper, we propose and analyze the mass-conservative characteristic finite difference method for solving two-sided space-fractional advection-diffusion equation. The predecessor numerical solutions are firstly computed by using the piecewise parabola method (PPM) which preserves the local mass conservation. Then, we solve the equations with the shifted Grünwald-Letnikov approximations by the splitting implicit characteristic difference scheme. By some auxiliary lemmas, we prove strictly that our schemes I and II are stable under the condition Δt = O(Δx2) based on the choice of the weight coefficient in L2-norm, respectively. Their error estimates are given and we prove our scheme I is of first-order and scheme II is second-order convergence in space, respectively. Due to the characteristic structure of the coefficient matrix, an efficient fast iterative algorithm is applied to our schemes with the computational complexity of only O(\(N \log N\)). Numerical experiments are used to verify our one-dimensional and two-dimensional theoretical analysis.

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Funding

This work was supported partially by the National Natural Science Foundation of China (Grant No. 61703250), Natural Science Foundation of Shandong Government (Grant No. ZR2021MA002) and Shandong Agricultural University.

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Authors and Affiliations

  1. School of Information Science and Engineering, Shandong Agricultural University, Taian, Shandong, 271018, China

    Tongtong Hang, Zhongguo Zhou, Hao Pan & Yan Wang

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  1. Tongtong Hang
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  4. Yan Wang
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Correspondence to Zhongguo Zhou.

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Hang, T., Zhou, Z., Pan, H. et al. The conservative characteristic difference method and analysis for solving two-sided space-fractional advection-diffusion equations. Numer Algor 92, 1723–1755 (2023). https://doi.org/10.1007/s11075-022-01363-2

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