A. Papini, ABOUT THE CENTRAL DIFFERENCE METHOD FOR SINGULARLY PERTURBED BOUNDARY-VALUE-PROBLEMS, Applied numerical mathematics, 17(3), 1995, pp. 333-346
In this paper we give a detailed analysis of the central difference sc
heme applied to the linear second-order equation epsilon x '' = a(t)x'
+ b(t)x + f(t), with two-point boundary conditions x(t(0)) = x(0) x(t
(f)) = x(f). We assume that a(t)< 0, so the solution x(t) may have a b
oundary layer in t(0). A class of nonuniform meshes is proposed, which
ensures accuracy in the layer plus stability and second-order converg
ence elsewhere.