FD method of arbitrary uniform order of accuracy for solving singularly perturbed boundary problems for second-order ordinary differential equations

Using a functional-discrete approach, three-point difference schemes of arbitrary order of accuracy are constructed for solving the Dirichlet problem for second-order ordinary differential equations (ODE) with a small parameter multiplying the leading derivative. The uniform convergence of the schemes with respect to the small parameter is proved, and a recursive algorithm for their realization is constructed. Bibliography:4 titles. Translated fromObchyslyuval’na ta Prykladna Matematyka, No. 77, 1993, pp. 35–43.