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<p>This manuscript presents a Quartic B-spline Method (QBSM) for the accurate estimation of numerical solutions to singularly perturbed third order boundary value problems (SPTOBVPs). The technique leverages a piecewise uniform mesh, constructed through the Fitted Mesh Technique (FMT), to enhance nodal point distribution within boundary layer regions. The convergence of proposed method are thoroughly investigated and found that it gives second-order convergence results. The efficacy of proposed method is demonstrated through the numerical examples, substantiating its theoretical results.</p>

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Numerical Solution of Third-Order Singularly Perturbed Boundary Value Problems Via Quartic B-Spline Method

  • 期刊论文

  • 发表日期：

    2025年12月29日

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  • Hradyesh Kumar Mishra,
  • Ram Kishun Lodhi

摘要

This manuscript presents a Quartic B-spline Method (QBSM) for the accurate estimation of numerical solutions to singularly perturbed third order boundary value problems (SPTOBVPs). The technique leverages a piecewise uniform mesh, constructed through the Fitted Mesh Technique (FMT), to enhance nodal point distribution within boundary layer regions. The convergence of proposed method are thoroughly investigated and found that it gives second-order convergence results. The efficacy of proposed method is demonstrated through the numerical examples, substantiating its theoretical results.