This paper deals with the robust numerical method for solving the singularly perturbed semilinear partial differential equation with the spatial delay. The quadratically convergent quasilinearization technique is used to linearize the semilinear term. It is formulated by discretization of the solution domain and then replacing the differential equation by finite difference approximation that in turn gives the system of algebraic equations. The method is shown to be first-order convergent. It is observed that the convergence is independent of the perturbation parameter. Numerical illustrations are investigated on model examples to support the theoretical results and the effectiveness of the method.

本文提出了一种求解带有空间滞后的奇摄动半线性偏微分方程的鲁棒数值方法。二次收敛拟线性化技术用于使半线性项线性化。它通过解域的离散化来表示，然后用有限差分近似代替微分方程，从而给出了代数方程组。该方法显示为一阶收敛。可以看出，收敛与扰动参数无关。在模型示例上研究了数值插图，以支持理论结果和方法的有效性。