| A nonlinear multistep method which bears the nature of the classical Adams-Bashforth-Moulton PC formula is developed to solve stiff initial value problems of the form y' = Ay + g(x,y).; It is shown that this method has properties of consistency, convergence and A-stability in the sense of Dahlquist. Several newly developed numerical techniques have been incorporated into this algorithm. A detailed analysis of its structure is also presented to enable us to implement this method in such a way that the step size and the order can be adjusted automatically.; Numerical results from extensive tests by a PECE mode of this method shows its efficiency and several advantages, such as no Jacobian evaluation is needed, much larger step sizes can be used and only a few matrix inversions are involved. |
