Runge–Kutta pairs of orders 8(7) with extended stability regions for addressing linear inhomogeneous systems

• Published in: Mathematical methods in the applied sciences Vol. 46; no. 4; pp. 4212 - 4224
• Main Authors: Busygin, Sergey, Fedorov, Ruslan, Karpukhina, Tamara, Kovalnogov, Vladislav N., Simos, Theodore E., Tsitouras, Charalampos
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 15.03.2023
• Subjects: Algorithms; Boundary value problems; differential evolution; heat transfer; Inhomogeneous systems; initial value problem; linear inhomogeneous; numerical solution; Optimization; plate movement; Runge-Kutta method; Stability; Truncation errors; vibrator
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.8750

The non‐stiff Initial Value Problem is a wider subject classified in Mathematics. Here, we consider an interesting subclass. Namely, the Linear Inhomogeneous system that shares constant coefficients. Runge–Kutta pairs of high orders are chosen in order to achieve stringent accuracies when solving these systems numerically. It is theoretically interesting to equip these methods with large stability intervals for addressing the problems at hand. Thus, at first, we present an explicit algorithm for deriving the coefficients of such pairs of orders eight and seven. Then we adjust this in an optimization precess for extending the stability region and simultaneously keep the principal truncation error as low as possible. The resulting pair outperforms other standard pairs in a series of relevant problems.