A class of generalized trapezoidal formulas for the numerical integration of

Abstract

The classical arithmetic mean (AM) trapezoidal formula is known to be A-stable. Recently, Chawla and Al-Zanaidi [1] described a modified arithmetic mean (MAM) trapezoidal formula which is L-stable. In the present paper we introduce a one-parameter family of generalized trapezoidal formulas (GTFs), which include both the AM and MAM trapezoidal formulas 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 formulas for the integration of examples of the stiff systems considered.

Keywords:

• Ordinary differential equations
• initial value problem
• trapezoidal formula
• generalized trapezoidal formula
• A-stability
• L-stability
• stiff systems

C.R. Category::

• G.1.7