A Boundary Value Approach For A Class Of Singularly Perturbed Problems With Spike-Type Contrast Structure

In this paper, a new boundary value method is presented for solving a class of singularly perturbed boundary value problems with spike-type contrast structure. For the internal layer problem, firstly, the original problem is parti-tioned into left and right problem from the transfer point at the internal layer region. Then, through the boundary value method, the left and right problems are converted into the non-singularly perturbed problems. And by the bound-ary layer correction technique, the original problem is directly converted into two non-singularly perturbed problems.There are four chapters in this paper. The first one contains a brief introduction to the background and significance of the study of the singularly perturbed problems with spike-type contrast structure, and the main problems discussed in this paper are also presented. The second one investigates the second-order semi-linear problem with spike-type contrast structure, and which can be solved by using the boundary value method. The third one is devoted to some numerical examples, and indicates the efficiency of the boundary value method by numerical tests. And the last one gives some results.