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.

A class of generalized trapezoidal formulas for the numerical integration of

Numerical solution of the Goursat problem by a nonlinear trapezoidal formula

Nonlinear trapezoidal formulae based on a variety of means other than the arithmetic and geometric means, ie harmonic, logarithmic, etc, for solving first order differential equations with specified initial values are presented The accuracy and stability properties of the methods are investigated and some conclusions drawn from a numerical example

A comparison of nonlinear trapezoidal formulae for solving initial value problems

A class of stable nonlinear trapezoidal formulas based on a variety of means for solving initial value problems of the form is developed. The accuracy and stability of the new formulas are investigated. Numerical tests are carried out to compare the results of the established methods with the results of the existing formulas.

On the numerical solution of by a class of nonlinear trapezoidal formulas

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

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

A new class of non-linear methods based on Euler's integration formula for the numerical solution of ordinary differential equations is presented. Considerations are given to the accuracy and stability of the proposed method and its applicability to stiff problems with supporting numerical evidence.

B. B. Sanugi

Papers

A comparison of numerical o.d.e. solvers based on arithmetic and geometric means