On the numerical solution of initial value problems for nonlinear trapezoidal formulas with different types

Abstract

In this paper, the local truncation errors of the trapezoidal formulas such as arithmetic mean (AM), geometric mean (GM), heronian mean (HeM), harmonic mean (HaM), contraharmonic mean (CoM), root mean square (RMS), logarithmic mean (LM) and centroidal mean (CeM) are investigated and the stability analysis of these formulas are found. Finally, it is applied to various initial value problems.