In this paper, an asymptotic numerical method based on a fitted finite difference scheme and the fourth-order Runge–Kutta method with piecewise cubic Hermite interpolation on Shishkin mesh is suggested to solve singularly perturbed boundary value problems for third-order ordinary differential equations of convection diffusion type with a delay. An error estimate is derived using the supremum norm and it is of almost first-order convergence. A nonlinear problem is also solved using the Newton’s quasi linearization technique and the present asymptotic numerical method. Numerical results are provided to illustrate the theoretical results.

中文翻译：

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三阶奇摄动对流扩散延迟微分方程的渐近数值方法

本文提出了一种基于拟合有限差分格式的渐近数值方法和在Shishkin网格上采用分段三次Hermite插值的四阶Runge–Kutta方法，以解决三阶对流常微分方程的奇摄动边值问题。有延迟的扩散类型。误差估计是使用最高范数得出的，几乎是一阶收敛的。还使用牛顿拟线性化技术和当前渐近数值方法来解决非线性问题。提供数值结果以说明理论结果。