Numerical Solution Of High Accuracy For Quasilinear Singularly Perturbed Convection-diffusion Problems

In this paper, we mainly study to solve quasilinear singularly perturbed convection diffusion boundary value problems from two parts as follows:(1) The first part, a class of hybrid difference schemes with variable weights on Bakhvalov-Shishkin mesh is proposed to compute the solution in quasilinear singularly perturbed convection-diffusion boundary value problems. First, we use hybrid difference schemes on Bakhvalov-Shishkin to study the general situation. We use the simple upwind scheme on the coarse part and central scheme on the fine part. Then, we define the discrete linear operator, and prove the discrete linear operator is an M-matrix. We get the uniform second-order O(N-2) using the comparison principle. Moreover, we improved the variable weights. Finally, numerical example support our error estimates.(2) In the second part, a class of hybrid difference schemes with variable weights on Bakhvalov-Shishkin mesh is proposed to compute the derivative in quasilinear singularly perturbed convection-diffusion boundary value problems. We use backward difference at xi-1/2, and get the uniform second-order O(N-2) according to the solution’s proof method. Then, we improve the previous papers in S mesh. Only if N is large enough, we have the hybrid scheme on S mesh and obtain uniform convergence of nearly second-order O(N-2ln2N). Last, we compare the S mesh and B-S mesh, and the error estimates of numerical solutions and numerical derivatives are all confirmed through our numerical experiments.