A-Stable Block ETRs/ETR2s Methods for Stiff ODEs

Yohanna Sani Awari


We present a class of fourth and sixth order A-stable block extended trapezoidal rule of first kind (ETRs) and extended trapezoidal rule of second kind (ETR2s) methods which are found to be adequate for the numerical integration of stiff ordinary differential equations. The single continuous formulation of this methods are evaluated at some grid and interior points yielding the multi-discrete schemes which are implemented in block form thereby generating simultaneously approximate solutions  at once without recourse to predictors. By this approach, the need for starters is eliminated. The stability properties of the block ETRs/ETR2s methods discussed and were shown to preserve the A-stability property of the trapezoidal rule, their absolute stability regions also presented. The newly derived block methods were implemented on five stiff systems of ordinary differential equations occurring in real life to show efficiency and accuracy.

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