Abstract: This paper presents basic idea to construct high order difference schemes for linear two order ordinary differential equations with boundary values. A six order tridiagonal OCI difference scheme is deduced and the singularity at ends of interval are treated by means of limited values. A six order tridiagonal OCI difference scheme on non-uniform mesh is adopted for layer problems. A large number of numerical experimental results show that this high order tridiagonal OCI difference scheme can solve singular problems, inherent instability problems, dichotomous instability problems, singular perturbation problems and oscillating problems very well.

Key words: tridiagonal OCT difference scheme, limited value method, non-uniform mesh, ODETPBVP, double back substitution