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<p>This work develops a novel high-order numerical scheme based on non-uniform meshes for the nonlinear time-fractional Benjamin-Bona-Mahony equations. The scheme achieves fourth-order spatial accuracy and second-order temporal accuracy, using a predictor–corrector strategy and a method of order reduction. Two compact difference operators are employed to approximate the nonlinear advection term <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(uu_x\)</EquationSource> </InlineEquation> and the linear dispersive term <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(u_{xx}\)</EquationSource> </InlineEquation>. Using the discrete energy method, we establish rigorous error estimates for the scheme in the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\( H^1 \)</EquationSource> </InlineEquation>-norm. To enhance computational efficiency, exponential sum approximations are utilized, and a fast algorithm is constructed and analyzed. The validity of the proposed schemes is demonstrated, and their performance is compared using two numerical examples.</p>

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Error analysis of a predictor-corrector compact difference scheme on nonuniform meshes for the time-fractional BBM equations

  • 期刊论文

  • 发表日期：

    2026年4月2日

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  • Wei Gou,
  • Maohua Ran,
  • Haodong Pu

摘要

This work develops a novel high-order numerical scheme based on non-uniform meshes for the nonlinear time-fractional Benjamin-Bona-Mahony equations. The scheme achieves fourth-order spatial accuracy and second-order temporal accuracy, using a predictor–corrector strategy and a method of order reduction. Two compact difference operators are employed to approximate the nonlinear advection term \(uu_x\) and the linear dispersive term \(u_{xx}\) . Using the discrete energy method, we establish rigorous error estimates for the scheme in the \( H^1 \) -norm. To enhance computational efficiency, exponential sum approximations are utilized, and a fast algorithm is constructed and analyzed. The validity of the proposed schemes is demonstrated, and their performance is compared using two numerical examples.