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<p>An efficient numerical scheme is developed for nonlinear time-space fractional diffusion equations. The exponential-sum-approximation technique is employed to approximate time fractional derivative, which reduces computational complexity and memory requirements compared to L1 method. The scheme utilizes a <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10915_2025_3047_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation>-matrix-based stiff-cut splitting strategy to accelerate the solving of linear systems. Unconditional stability and first-order convergence are rigorously established. Numerical experiments confirm the error analysis and demonstrate the effectiveness of the proposed method.</p>

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Efficient and Unconditionally Stable Stiff-Cut Scheme For Nonlinear Time-Space Fractional Diffusion Equations

  • 期刊论文

  • 发表日期：

    2025年9月5日

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  • Lu-Yao Sun,
  • Siu-Long Lei,
  • Hai-Wei Sun

摘要

An efficient numerical scheme is developed for nonlinear time-space fractional diffusion equations. The exponential-sum-approximation technique is employed to approximate time fractional derivative, which reduces computational complexity and memory requirements compared to L1 method. The scheme utilizes a \(\tau \) τ -matrix-based stiff-cut splitting strategy to accelerate the solving of linear systems. Unconditional stability and first-order convergence are rigorously established. Numerical experiments confirm the error analysis and demonstrate the effectiveness of the proposed method.