Abstract A numerical technique has been developed for integrating the one-dimensional steady state premixed laminar flame equations. A global finite difference approach is used in which the nonlinear difference equations are solved by a damped-modified Newton method. An assumed temperature profile helps to generate a converged numerical solution on an initial coarse grid. Mesh points are inserted in regions where the solution profiles exhibit high gradient and high curvature activity. These features are discussed and illustrated in the paper, and the method is used to calculate the temperature and species profiles of several laboratory flames.