Generalized RK integrators for solving class of sixth-order ordinary differential equations

Abstract

In this paper, the classical RK integrators for solving quasi-linear(QL) ordinary differential equations (ODEs) up to 5th-order have been generalized to solve class of 6th-order ODEs. The novel contribution of this work is the derivation of two efficient direct integrators for solving class of ODEs. Non-linear equations of order conditions (OCs) for the proposed RKM methods have derived up to the 7th-order using Taylor expansion. Two RKM integrators of three-stages, 5th-order and four-stages, 6th-order have been derived depend on these OCs. The proposed integrates have been tested using some implementations in order to compare them with classical methods which show that the proposed integrators are less than classical RK methods in term of time complexity and function evaluations.

Subject Classification:

• Primary65-XX
• Secondary 65L05

Keywords:

• RK
• RKN
• RKD
• RKM
• RKT
• Sixth-order
• DEs
• ODEs
• Taylor expansion