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Abstract <p>The aim of this paper is to construct a fourth-order compact finite difference (CFD) scheme for solving 2D time-fractional mixed diffusion and diffusion-wave equation, in which the fractional derivative is denoted by Caputo–Fabrizio (C–F) sense. We prove the stability and error estimation theorems for the CFD scheme. It is worth pointing out that the convergence order of CFD scheme is <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11470_2025_2326_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="116" /> </InlineMediaObject> <EquationSource Format="TEX">\(O({{\tau }^{2}} + h_{x}^{4} + h_{y}^{4})\)</EquationSource> <!--ComMat2570127An-m1--> </InlineEquation>, where <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11470_2025_2326_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau \)</EquationSource> <!--ComMat2570127An-m2--> </InlineEquation>, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11470_2025_2326_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\({{h}_{x}}\)</EquationSource> <!--ComMat2570127An-m3--> </InlineEquation>, and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11470_2025_2326_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\({{h}_{y}}\)</EquationSource> <!--ComMat2570127An-m4--> </InlineEquation> are the time step size, space step size (for <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11470_2025_2326_Article_IEq5.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(x\)</EquationSource> <!--ComMat2570127An-m5--> </InlineEquation>) and space step size (for <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11470_2025_2326_Article_IEq6.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(y\)</EquationSource> <!--ComMat2570127An-m6--> </InlineEquation>), respectively. Some relevant examples are indicated to verify the correctness of theoretical analysis and the effectiveness of CFD scheme.</p>

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A High-Order Accurate Scheme for 2D Fractional Mixed Diffusion and Diffusion-Wave Equation

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • Wenjing An,
  • Leilei Wei,
  • Xindong Zhang,
  • Peng Li

摘要

Abstract

The aim of this paper is to construct a fourth-order compact finite difference (CFD) scheme for solving 2D time-fractional mixed diffusion and diffusion-wave equation, in which the fractional derivative is denoted by Caputo–Fabrizio (C–F) sense. We prove the stability and error estimation theorems for the CFD scheme. It is worth pointing out that the convergence order of CFD scheme is \(O({{\tau }^{2}} + h_{x}^{4} + h_{y}^{4})\) , where \(\tau \) , \({{h}_{x}}\) , and \({{h}_{y}}\) are the time step size, space step size (for \(x\) ) and space step size (for \(y\) ), respectively. Some relevant examples are indicated to verify the correctness of theoretical analysis and the effectiveness of CFD scheme.