We consider a quasilinear singularly perturbed parametrized problem with integral boundary condition. To solve the problem numerically, the discretization comprises of an implicit Euler scheme for the quasilinear problem and a composite right rectangle rule for the integral boundary condition. We establish a posteriori error estimate for the discrete problem that holds true uniformly in the small perturbation parameter. Further, we rectify the shortcomings of a posteriori error estimation in L.-B. Liu et al. (Numerical Algorithms 83:719–739, 2019) for a different class of problems. Numerical experiments are performed and results are reported for validation of the theoretical error estimates.

我们考虑具有积分边界条件的拟线性奇异摄动参数化问题。为了数值求解该问题，离散化包括拟线性问题的隐式欧拉格式和积分边界条件的复合右矩形规则。我们为离散问题建立了一个后验误差估计，它在小扰动参数中一致成立。此外，我们纠正了 L.-B 中后验误差估计的缺点。刘等人。( Numerical Algorithms 83:719–739, 2019) 用于不同类别的问题。进行数值实验并报告结果以验证理论误差估计。