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<p>This paper presents an alternating direction implicit (ADI) difference scheme on graded meshes for solving three-dimensional (3D) multi-term nonlinear subdiffusion equations with constant coefficients. The temporal discretization employs L1 approximation on graded meshes for the Caputo fractional derivative, while spatial discretization uses central difference method on uniform meshes. Theoretical analysis are presented concluding existence, uniqueness, stability and convergence of the proposed scheme. An <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\alpha _p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>α</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation>-robustness analysis demonstrates that the error bound remains effectiveness as <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\alpha _p\rightarrow 1^-.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>α</mi> <mi>p</mi> </msub> <mo stretchy="false">→</mo> <msup> <mn>1</mn> <mo>-</mo> </msup> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> Numerical experiments with two test cases confirm the theoretical results.</p>

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Error estimation of \(\alpha _p\)-robust ADI difference scheme on graded meshes for the three-dimensional nonlinear multiterm subdiffusion equation with constant coefficients

  • 期刊论文

  • 发表日期：

    2025年12月22日

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  • Zhaoxiang Zhang,
  • Xuehua Yang

摘要

This paper presents an alternating direction implicit (ADI) difference scheme on graded meshes for solving three-dimensional (3D) multi-term nonlinear subdiffusion equations with constant coefficients. The temporal discretization employs L1 approximation on graded meshes for the Caputo fractional derivative, while spatial discretization uses central difference method on uniform meshes. Theoretical analysis are presented concluding existence, uniqueness, stability and convergence of the proposed scheme. An \(\alpha _p\) α p -robustness analysis demonstrates that the error bound remains effectiveness as \(\alpha _p\rightarrow 1^-.\) α p → 1 - . Numerical experiments with two test cases confirm the theoretical results.