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<p>This work presents the convergence of time-filtered backward differentiation formula (BDF) methods up to fourth-order time accuracy for the molecular beam epitaxial (MBE) equation without slope selection. With the help of the discrete orthogonal convolution kernels, some concise <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 error estimates are established via the discrete energy technique. To the best of our knowledge, this is the first time such type <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> norm error estimates of time-filtered BDF2 and time-filtered BDF3 schemes are obtained for a nonlinear parabolic equation. Numerical examples are included to show the effectiveness of the proposed methods.</p>

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Convergence analysis of time-filtered backward differentiation methods up to fourth-order for the molecular beam epitaxial model without slope selection

  • 期刊论文

  • 发表日期：

    2026年4月8日

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  • Jiexin Wang,
  • Hong-lin Liao

摘要

This work presents the convergence of time-filtered backward differentiation formula (BDF) methods up to fourth-order time accuracy for the molecular beam epitaxial (MBE) equation without slope selection. With the help of the discrete orthogonal convolution kernels, some concise \(L^2\) L 2 norm error estimates are established via the discrete energy technique. To the best of our knowledge, this is the first time such type \(L^2\) L 2 norm error estimates of time-filtered BDF2 and time-filtered BDF3 schemes are obtained for a nonlinear parabolic equation. Numerical examples are included to show the effectiveness of the proposed methods.