Uniformly convergent hybrid schemes for solutions and derivatives in quasilinear singularly perturbed BVPs

摘要

In this paper, a class of hybrid difference schemes with variable weights on Bakhvalov-Shishkin mesh is proposed to compute both the solution and the derivative in quasilinear singularly perturbed convection-diffusion boundary value problems. The parameter-uniform second-order convergence of approximating to the solution and the derivative on Bakhvalov-Shishkin mesh and that of nearly second-order on Shishkin mesh are proved clearly by use of an (l_∞,l_1)-stability property, where the former sufficient conditions for uniform convergence are modestly relaxed on Bakhvalov-Shishkin mesh and are clarified on Shishkin mesh. The numerical examples support the proposed schemes with new sufficient conditions and their error estimates.