Scholarlink

<p>In this present manuscript, the one-dimensional coupled Korteweg-de Vries (CKdV) equation is solved arithmetically with the practice of quintic Uniform Algebraic Trigonometric (UAT) tension B-spline along employing differential quadrature method (DQM). The discretisation of partial derivatives and value of weighting coefficients is accomplished with the convention of UAT spline, giving the ordinary differential equations. These ODEs are solved with the Runge–Kutta method. The competence and accurateness of the technique is tested by the use of the error norms <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3100_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\({L}_{\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3100_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\({L}_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> errors and the three lowest invariants <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3100_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\({I}_{1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>I</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3100_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\({I}_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>I</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3100_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\({I}_{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>I</mi> <mn>3</mn> </msub> </math></EquationSource> </InlineEquation>. New regime of order six that is quintic Uniform Algebraic Trigonometric (UAT) tension B-spline is proposed. This quintic spline has never been used before to solve the differential equation. The accomplished numerical results are presented with 2D and 3D figures, where the comparison with the exact solution is also demonstrated. It is clinched that the presented technique is a well-organized and operative procedure for elucidating the CKdV equations and similarly for the more partial differential equations.</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

Quintic uniform algebraic trigonometric tension B-spline differential quadrature approach for the solution of coupled Korteweg-de Vries equation

  • 期刊论文

  • 发表日期：

    2025年2月17日

查看全文
  • Navneet Kaur,
  • Varun Joshi

摘要

In this present manuscript, the one-dimensional coupled Korteweg-de Vries (CKdV) equation is solved arithmetically with the practice of quintic Uniform Algebraic Trigonometric (UAT) tension B-spline along employing differential quadrature method (DQM). The discretisation of partial derivatives and value of weighting coefficients is accomplished with the convention of UAT spline, giving the ordinary differential equations. These ODEs are solved with the Runge–Kutta method. The competence and accurateness of the technique is tested by the use of the error norms \({L}_{\infty }\) L ∞ and \({L}_{2}\) L 2 errors and the three lowest invariants \({I}_{1}\) I 1 , \({I}_{2}\) I 2 and \({I}_{3}\) I 3 . New regime of order six that is quintic Uniform Algebraic Trigonometric (UAT) tension B-spline is proposed. This quintic spline has never been used before to solve the differential equation. The accomplished numerical results are presented with 2D and 3D figures, where the comparison with the exact solution is also demonstrated. It is clinched that the presented technique is a well-organized and operative procedure for elucidating the CKdV equations and similarly for the more partial differential equations.