The numerical solution of a quasilinear singularly perturbed problem with an integral boundary condition is considered. For discretizing the differential equation, we use the backward Euler formula and for the integral boundary condition the left rectangle formula is constructed on an arbitrary nonuniform mesh. Based on the truncation error analysis and mesh equidistribution principle, a suitable monitor function is chosen to obtain an adaptive grid. Furthermore, the convergence analysis of our discretization scheme on an adaptive grid before and after Richardson extrapolation is carried out, which is shown that the use of Richardson extrapolation improves the uniform accuracy in the discrete maximum norm from first-order to second-order. Finally, some numerical results are given to illustrate the theoretical results.

考虑具有积分边界条件的拟线性奇摄动问题的数值解。为了离散化微分方程，我们使用后向Euler公式，对于积分边界条件，左矩形公式构建在任意非均匀网格上。基于截断误差分析和网格平均分布原理，选择合适的监测函数以获得自适应网格。此外，在Richardson外推之前和之后，在自适应网格上对离散化方案进行了收敛性分析，结果表明，使用Richardson外推可以提高离散最大范数从一阶到二阶的一致精度。最后，给出一些数值结果来说明理论结果。