Scholarlink

<p>One of the major challenges in numerical analysis for fractional initial value problems is maintaining high-order accuracy when the solutions are non-smooth. The limited regularity of the solutions often reduces the convergence rates of standard spectral collocation methods. To address this, we develop a novel spectral collocation method for solving nonlinear fractional differential equations, utilizing nonstandard fractional Jacobi functions as the basis functions. A key advantage of using these non-standard basis functions is their ability to effectively handle the non-locality and the low regularity of the solution. We demonstrate through weighted <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2633_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\bf\it L^2\)</EquationSource> </InlineEquation> convergence analysis and numerical experiments that the proposed method achieves high-order accuracy for fractional initial value problems with low regular solutions.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Improved spectral method for the nonsmooth solutions of nonlinear fractional differential equations

  • 期刊论文

  • 发表日期：

    2025年9月3日

查看全文
  • Mahmoud A. Zaky,
  • Omar Abu Arqub

摘要

One of the major challenges in numerical analysis for fractional initial value problems is maintaining high-order accuracy when the solutions are non-smooth. The limited regularity of the solutions often reduces the convergence rates of standard spectral collocation methods. To address this, we develop a novel spectral collocation method for solving nonlinear fractional differential equations, utilizing nonstandard fractional Jacobi functions as the basis functions. A key advantage of using these non-standard basis functions is their ability to effectively handle the non-locality and the low regularity of the solution. We demonstrate through weighted \(\bf\it L^2\) convergence analysis and numerical experiments that the proposed method achieves high-order accuracy for fractional initial value problems with low regular solutions.