This work builds the order accuracy conditions for Three-Derivative Two-Step Runge-Kutta Methods (ThDTSRK) and develop a general form of the order accuracy conditions (p < 8). We propose A-stability property theory for ThDTSRK methods, and find optimal stability coefficients. The stability regions of ThDTSRK methods are displayed in file (A-stable-ThDTSRK.nb). The order of convergence for ThDTSRK methods are tested on the Prothero-Robinson problem, the order accuracy are in line with the expectation.
The data and code correspond to our article. Qin, X.; Yu, J.; Yan, C. Derivation of Three-Derivative Two-Step Runge–Kutta Methods. Mathematics 2024, 12, 711. https://doi.org/10.3390/math12050711