A SIXTH ORDER NUMERICAL METHOD FOR A CLASS OF NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS

In this paper, we are concerned with the numerical solution of a class of nonlinear two-point boundary value problems with general boundary conditions. We propose a new numerical method of sixth order accuracy by integrating compact finite difference methods with the Green's function approach. It is the first sixth order accurate numerical scheme on no-uniform grids for the problem. We also give numerical results of some practical problems including reaction-diffusion equations. It is remarked that our numerical method is also efficient for layer equations.