This work is the result of our article[1] and builds the order accuracy conditions for Three-Derivative Runge-Kutta Methods (ThDRK). There are two devices to build the order conditions for Runge-Kutta methods: rooted trees[2] and Albrecht's approach[3]. The code file shows the order accuracy conditions for ThDRK by Albrecht's approach and verified the coefficients are equivalent for the conditions by rooted trees theory[4].
*.nb file is run on Wolfram Mathematica 12, it may be able to run on other versions.
*.cpp files are the code for our numerical experiments.
[1] Qin, X., Jiang, Z., Yu, J. et al. Strong stability-preserving three-derivative Runge–Kutta methods. Comp. Appl. Math. 42, 171 (2023). https://doi.org/10.1007/s40314-023-02285-y
[2] Butcher J C. Trees and numerical methods for ordinary differential equations[J]. Numerical Algorithms, 2010, 53(2): 153-170.
[3] Albrecht P. The Runge–Kutta theory in a nutshell[J]. SIAM Journal on Numerical Analysis, 1996, 33(5): 1712-1735.
[4] Turacı M Ö, Öziş T. Derivation of three-derivative Runge-Kutta methods[J]. Numerical Algorithms, 2017, 74(1): 247-265.