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An examination of a singularly perturbed BVP is conducted, focusing on a linear parabolic second-order DDE with reaction-diffusion characteristics and a discontinuous source term. This investigation takes place within the rectangular domain \((0,2)\times (0,T]\) . Perturbation parameter that multiplies highest order derivative term and discontinuity occurred in the source term give rise to boundary and interior layers respectively. A numerical method that which combines Crank Nicolson scheme for time discretisation and classical finite difference scheme for space discretisation in Shishkin piecewise uniform mesh is constructed. Numerical experiments are presented to support the theory established.

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Crank-Nicolson Scheme for Singularly Perturbed Delay Differential Equation with a Discontinuous Source Term

  • 会议论文

  • 发表日期：

    2025年

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  • Parthiban Saminathan,
  • Franklin Victor

摘要

An examination of a singularly perturbed BVP is conducted, focusing on a linear parabolic second-order DDE with reaction-diffusion characteristics and a discontinuous source term. This investigation takes place within the rectangular domain \((0,2)\times (0,T]\) . Perturbation parameter that multiplies highest order derivative term and discontinuity occurred in the source term give rise to boundary and interior layers respectively. A numerical method that which combines Crank Nicolson scheme for time discretisation and classical finite difference scheme for space discretisation in Shishkin piecewise uniform mesh is constructed. Numerical experiments are presented to support the theory established.