NEW L-STABLE MODIFIED TRAPEZOIDAL FORMULAS FOR THE NUMERICAL-INTEGRATION OF Y'=F(X,Y)

We present a new class of trapezoidal formulas obtained by suitably mo difying the classical arithmetic mean formula and the recently propose d geometric and harmonic mean formulas. Interestingly, when applied to the test equation, a modified trapezoidal formula leads to a single l inear 1-step recurrence. We show that each of these modified trapezoid al formulas is second order and L-stable. For the integration of auton omous problems, both the modified geometric and harmonic mean trapezoi dal formulas are well-defined around f = 0, at least for sufficiently small step-lengths.