High-order three-point schemes for boundary value problems. II: nonlinear problems

摘要

A highly accurate method for solving nonlinear boundary value problems of the convection-diffusion type is presented. It is shown that the rate of convergence of the present method is very rapid, superior to that of the classical central difference methods. Its main feature is that the converged solution can be achieved within a reasonable amount of iterations for any small value of the mesh diffusion coefficient. All these features are supported by comparisons that are presented for several example problems.