Runge–Kutta pairs of orders 9(8) for use in quadruple precision computations.

Runge–Kutta embedded pairs of high algebraic order are frequently utilized when strict tolerances are required. When creating such pairings of orders nine and eight for use in double precision arithmetic, numerous conditions are often satisfied. First and foremost, we strive to keep the coefficients' magnitudes small to prevent accuracy loss. We may, however, allow greater coefficients when working with quadruple precision. Then, we may build pairs of orders 9 and 8 with significantly smaller truncation errors. In this paper, a novel pair is generated that, as predicted, outperforms state-of-the-art pairs of the same orders in a collection of important problems. [ABSTRACT FROM AUTHOR]