论文标题
两参数的参数统一方法与不连续数据奇异的边界价值问题
A parameter uniform method for two-parameter singularly perturbed boundary value problems with discontinuous data
论文作者
论文摘要
在一个维度中考虑了一个两参数的奇异扰动问题和对流系数。对流系数和源项在域中的某个点都是不连续的。扰动参数的存在导致边界处的边界层。同样，由于内部点的数据不连续，内部层发生。适当定义的Shishkin-Bakhvalov网格上的上风方案用于解析边界层和内部层。在不连续性点使用三点公式。所提出的方法具有一阶参数均匀收敛。在某些测试问题上使用数值方法对得出的理论错误估计进行了验证。数值结果验证了提出的主张。 Shiskin-Bakhvalov网格的使用有助于实现一阶收敛，与Shishkin网格不同，由于对数项，收敛顺序会恶化。
A two-parameter singularly perturbed problem with discontinuous source and convection coefficient is considered in one dimension. Both convection coefficient and source term are discontinuous at a point in the domain. The presence of perturbation parameters results in boundary layers at the boundaries. Also, an interior layer occurs due to the discontinuity of data at an interior point. An upwind scheme on an appropriately defined Shishkin-Bakhvalov mesh is used to resolve the boundary layers and interior layers. A three-point formula is used at the point of discontinuity. The proposed method has first-order parameter uniform convergence. Theoretical error estimates derived are verified using the numerical method on some test problems. Numerical results authenticate the claims made. The use of the Shiskin-Bakhvalov mesh helps achieve the first-order convergence, unlike the Shishkin mesh, where the order of convergence deteriorates due to a logarithmic term.
