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<p>In this paper, a three-level linear and compact finite difference scheme with fourth-order accuracy for the generalized Degasperis–Procesi (DP) equation is proposed. The difference scheme is conservative for the discrete energy. The solvability, a priori estimates, convergence and stability of the numerical solution are discussed in detail. The convergence rate is <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2884_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="79" /> </InlineMediaObject> <EquationSource Format="TEX">\(O(\tau ^{2}+h^{4})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mi>τ</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>h</mi> <mn>4</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. Some numerical results are provided to confirm that the scheme is effective and reliable.</p>

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A Compact and Energy Conservative Difference Scheme for the Generalized Degasperis–Procesi Equation

  • 期刊论文

  • 发表日期：

    2025年6月24日

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  • Xiaofeng Wang

摘要

In this paper, a three-level linear and compact finite difference scheme with fourth-order accuracy for the generalized Degasperis–Procesi (DP) equation is proposed. The difference scheme is conservative for the discrete energy. The solvability, a priori estimates, convergence and stability of the numerical solution are discussed in detail. The convergence rate is \(O(\tau ^{2}+h^{4})\) O ( τ 2 + h 4 ) . Some numerical results are provided to confirm that the scheme is effective and reliable.