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<p>The differential Stein matrix equations (DSE) play a pivotal role in various scientific and engineering applications. In this study, we introduce a method to express the solutions of these equations. Our approach involves employing the Chebyshev collocation CC method to effectively address the DSE. Additionally, we provide an in-depth analysis of the errors associated with the proposed methods, uncovering their spectral rate of convergence. To demonstrate the efficacy of our proposed framework, we conducted numerical experiments that clearly illustrate the efficiency and reliability of these methods. It’s observed that augmenting the parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2555_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(m\)</EquationSource> </InlineEquation> results in reduced errors across. Furthermore, one can estimate these errors by solving the matrix differential equations designed for error estimation. All of the numerical computations have been performed on a PC by running some programs written in MATLAB software.</p>

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Numerical approach for solving the differential Stein matrix equations

  • 期刊论文

  • 发表日期：

    2025年6月18日

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  • Lakhlifa Sadek

摘要

The differential Stein matrix equations (DSE) play a pivotal role in various scientific and engineering applications. In this study, we introduce a method to express the solutions of these equations. Our approach involves employing the Chebyshev collocation CC method to effectively address the DSE. Additionally, we provide an in-depth analysis of the errors associated with the proposed methods, uncovering their spectral rate of convergence. To demonstrate the efficacy of our proposed framework, we conducted numerical experiments that clearly illustrate the efficiency and reliability of these methods. It’s observed that augmenting the parameter \(m\) results in reduced errors across. Furthermore, one can estimate these errors by solving the matrix differential equations designed for error estimation. All of the numerical computations have been performed on a PC by running some programs written in MATLAB software.