A CLASS OF GENERALIZED TRAPEZOIDAL FORMULAS FOR THE NUMERICAL-INTEGRATION OF Y'=F(X,Y)

The classical arithmetic mean (AM) trapezoidal formula is known to be A-stable. Recently, Chawla and Al-Zanaidi [1] described a modified ari thmetic mean (MAM) trapezoidal formula which is L-stable. In the prese nt paper we introduce a one-parameter family of generalized trapezoida l formulas (GTFs), which include both the AM and MAM trapezoidal formu las as special cases. A GTF can switch from an A-stable to an L-stable method depending on parameter values, and it is shown to perform, for certain selections of the parameter values, better than AM and MAM fo rmulas for the integration of examples of the stiff systems considered .