New L-stable modified trapezoidal formulas for the numerical integration of Y¹=f(x, y)

Abstract

We present a new class of trapezoidal formulas obtained by suitably modifying the classical arithmetic mean formula and the recently proposed geometric and harmonic mean formulas. Interestingly, when applied to the test equation, a modified trapezoidal formula leads to a single linear 1-step recurrence. We show that each of these modified trapezoidal formulas is second order and L-stable. For the integration of autonomous problems, both the modified geometric and harmonic mean trapezoidal formulas are well-defined around f=0, at least for sufficiently small step-lengths

Keywords:

• Ordinary differential equations
• initial value problem
• modified trapezoidal formulas
• stiffness
• L-stability

C.R.Categories:

• G.1.7