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<p>In this paper, we explore the strong stability preserving (SSP) conditions for implicit second derivative multistep methods (SDMMs) when forward Euler condition is coupled with different second derivative conditions. We construct optimal SSP implicit SDMMs up to order <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p=8\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>=</mo> <mn>8</mn> </mrow> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(k \le 10\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>≤</mo> <mn>10</mn> </mrow> </math></EquationSource> </InlineEquation> steps, which have larger SSP coefficients than the class of implicit linear multistep methods. Numerical experiments confirm that the proposed methods are capable in solving stiff problems preserving the positivity property without producing spurious oscillations.</p>

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High order strong stability preserving implicit second derivative multistep methods

  • 期刊论文

  • 发表日期：

    2025年12月18日

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  • Pari Khakzad,
  • Gholamreza Hojjati,
  • Ali Abdi

摘要

In this paper, we explore the strong stability preserving (SSP) conditions for implicit second derivative multistep methods (SDMMs) when forward Euler condition is coupled with different second derivative conditions. We construct optimal SSP implicit SDMMs up to order \(p=8\) p = 8 for \(k \le 10\) k ≤ 10 steps, which have larger SSP coefficients than the class of implicit linear multistep methods. Numerical experiments confirm that the proposed methods are capable in solving stiff problems preserving the positivity property without producing spurious oscillations.