Abstract: Self-starting methods such as the Runge-Kutta methods are often used for the solution of engineering problems on a computer because they need no special starting method and are therefore easy to program. Also the Runge-Kutta methods give an automatic procedure for adjusting the step-size, which again makes for easy use by a non-specialist. However, there are three major disadvantages of the Runge-Kutta methods. An important disadvantages of this method is that, the form of the error term is extremely complicated and can not easily be used for the estimation of the truncation error or determine a suitable step-size. Another undesirable feature of this method is the large number of derivative evaluation required per-step, this makes it time-consuming. The third problem associated with the method is that, it has proved inadequate for stiff systems. Fatokun, in earlier reports proposed a continuous approach for deriving self-starting multistep methods for solving initial value problems of ordinary differential equations. In this study we present an implementation procedure of an order seven integration method for initial value problems. Using the SCILAB to resolve the generated matrices and consequently a FORTRAN code was used to run the block method. The result shows that the method is convenient and easy to use. It needs no other single step method for the implementation of the seven-step method. The graphs of the region of Absolute Stability are also presented for each grid point.
J.O. Fatokun and G.I.O. Aimufua , 2007. Implementation of an Order Seven Self-Starting Multistep Methods Using Scilab and Fortran Codes. International Journal of Soft Computing, 2: 320-324.