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<p>The space-fractional KdV-Burgers equation is a nonlocal nonlinear partial differential equation, which is not easy to solve by proper generalized decomposition (PGD). In this paper, we propose a preconditioner to assist PGD. Combined with a variable transformation and a fixed point iteration, our approach correctly capture the shock wave propagation. It is a nice surprise that delicate artificial boundary treatment is not required. Moreover, the proposed method allows much larger time grid size than standard time-marching schemes.</p>

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Shock Wave Propagation in Space-Fractional KdV-Burgers Equation Simulated by Preconditioned Proper Generalized Decomposition

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Xinyi Guan,
  • Shaoqiang Tang

摘要

The space-fractional KdV-Burgers equation is a nonlocal nonlinear partial differential equation, which is not easy to solve by proper generalized decomposition (PGD). In this paper, we propose a preconditioner to assist PGD. Combined with a variable transformation and a fixed point iteration, our approach correctly capture the shock wave propagation. It is a nice surprise that delicate artificial boundary treatment is not required. Moreover, the proposed method allows much larger time grid size than standard time-marching schemes.