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<p>Recently, the class of Runge-Kutta type methods named Fractional HBVMs (FHBVMs) has been introduced for the numerical solution of initial value problems of fractional differential equations, and a corresponding <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10915_2025_3006_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="65" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {Matlab}^{\copyright }\,\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mtext>Matlab</mtext> <mi mathvariant="normal">©</mi> </msup> <mspace width="0.166667em" /> </mrow> </math></EquationSource> </InlineEquation> software has been released. Though an error analysis has already been given, a corresponding linear stability analysis is still lacking. We here provide such an analysis, together with some improvements concerning the mesh selection. This latter has been implemented into a new version of the code, which is available on the web.</p>

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Analysis and implementation of collocation methods for fractional differential equations

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年7月28日

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  • Luigi Brugnano,
  • Gianmarco Gurioli,
  • Felice Iavernaro,
  • Mikk Vikerpuur

摘要

Recently, the class of Runge-Kutta type methods named Fractional HBVMs (FHBVMs) has been introduced for the numerical solution of initial value problems of fractional differential equations, and a corresponding \(\hbox {Matlab}^{\copyright }\,\) Matlab © software has been released. Though an error analysis has already been given, a corresponding linear stability analysis is still lacking. We here provide such an analysis, together with some improvements concerning the mesh selection. This latter has been implemented into a new version of the code, which is available on the web.