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In this chapter, we have considered a class of singularly perturbed one-dimensional transport equations. It is a kind of hyperbolic delay differential equations. To solve this class of problems, we have applied unconditionally stable finite difference scheme, that is, backward-time backward-space scheme on a special type of non-uniform mesh, called Shishkin mesh. Finally, we have shown that order of convergence of the current approach is almost one in both spatial and temporal dimensions. Numerical examples are provided to validate the theoretical findings.

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Computational Study on Singularly Perturbed 1D Transport Equations with Space Delay Argument

  • 章节

  • 发表日期：

    2026年

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  • Santosh Kumar Sahani,
  • S. Padhmanaban,
  • V. Subburayan

摘要

In this chapter, we have considered a class of singularly perturbed one-dimensional transport equations. It is a kind of hyperbolic delay differential equations. To solve this class of problems, we have applied unconditionally stable finite difference scheme, that is, backward-time backward-space scheme on a special type of non-uniform mesh, called Shishkin mesh. Finally, we have shown that order of convergence of the current approach is almost one in both spatial and temporal dimensions. Numerical examples are provided to validate the theoretical findings.