Numerical study of third-order ordinary differential equations using a new class of two derivative Runge-Kutta type methods - Lee, Khai Chien; Senu, Norazak; Ahmadian, Ali; Ibrahim, Siti Nur Iqmal; Baleanu, D. (Elsevier, 2020)
This study introduces new special two-derivative Runge-Kutta type (STDRKT) methods involving the fourth derivative of the solution for solving third-order ordinary differential equations. In this regards, rooted tree theory and the corresponding B-series theory is proposed to derive order conditions for STDRKT methods. Besides, explicit two-stages fifth order and three-stages sixth order STDRKT methods are derived and stability,consistency and convergence of STDRKT methods are analysed in details. Accuracy and effectiveness of the proposed techniques are validated by a number of various test problems and compared to existing methods in the literature.