The layer-resolving transformation and mesh generation for quasilinear singular perturbation problems

The relationship is analyzed between layer-resolving transformations and mesh-generating functions for numerical solution of singularly perturbed boundary-value problems. The analysis is carried out for one-dimensional quasilinear problems without turning points, which are discretized by first-order finite-difference schemes. It is proved that if a general layer-resolving function is used to generate the discretization mesh, then the numerical solution converges uniformly in the perturbation parameter.