Scholarlink

<p>Riesz space-fractional reaction-dispersion equations (RSFRDEs) arise in numerous application areas. In this paper, we propose efficient fourth-order numerical methods for solving the RSFRDEs with variable coefficients on a finite domain. The Crank-Nicolson difference scheme is utilized to discretize the temporal derivative, while the fourth-order fractional centered difference operator is employed to discretize the spatial fractional derivatives in RSFRDEs. We analyze the stability and convergence of the difference schemes using 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. The coefficient matrix of the discretized linear system has a structure given by the sum of a diagonal matrix and a diagonal-times-Toeplitz matrix. We develop a scaled Toeplitz splitting (STS) iteration method and propose an STS-based polynomial preconditioner, and then employ the Krylov subspace iteration methods to solve the linear system. The spectral distribution of the preconditioned matrix is analyzed, and some theoretical results are presented. Numerical results demonstrate the effectiveness of the proposed methods.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

An efficient preconditioned iterative method for solving discretized fourth-order Riesz spatial fractional reaction-dispersion equations with variable coefficients

  • 期刊论文

  • 发表日期：

    2026年1月23日

查看全文
  • Shi-Ping Tang,
  • Yu-Mei Huang

摘要

Riesz space-fractional reaction-dispersion equations (RSFRDEs) arise in numerous application areas. In this paper, we propose efficient fourth-order numerical methods for solving the RSFRDEs with variable coefficients on a finite domain. The Crank-Nicolson difference scheme is utilized to discretize the temporal derivative, while the fourth-order fractional centered difference operator is employed to discretize the spatial fractional derivatives in RSFRDEs. We analyze the stability and convergence of the difference schemes using the discrete \(L^{2}\) L 2 -norm. The coefficient matrix of the discretized linear system has a structure given by the sum of a diagonal matrix and a diagonal-times-Toeplitz matrix. We develop a scaled Toeplitz splitting (STS) iteration method and propose an STS-based polynomial preconditioner, and then employ the Krylov subspace iteration methods to solve the linear system. The spectral distribution of the preconditioned matrix is analyzed, and some theoretical results are presented. Numerical results demonstrate the effectiveness of the proposed methods.