Abstract
In Davie [3] paper, he assumed that the matrix (b(ik)(x)) is invertible for all x, but in this paper we will show how we could control the matrix which is non-invertible for some x using the (Combined method). We describe a method for non-invertibility case (Combined method) and we investigate its convergence order which will give O(h3/4( )root vertical bar log(h)vertical bar) under some conditions. Moreover we compare the computational results for the combined method with its theoretical error bound and we have obtained a good agreement between them.