Abstract
In this study, the development of direct explicit numerical integrators of RK-type for solving a class of ninth-order ordinary differential equations (ODEs) to develop the computational efficiency of the methods. The objective of this paper is to generalize the numerical integrators of RK type for solving classes of ODEs of orders up to eighth-order ODEs. Using the approach of Taylor-expansion, we have derived the order-conditions (OCs) for RKM integrators. Based on ... these OCs, developed method of ninth-order with five-stage has been derived. The zero stability of RKM integrator is proven. Stability .... polynomial of RKM integrator for test problem has been introduced. The advantage and the efficiency of the proposed method have been .. shown clearly using the numerical results which are agree well with .. analytical solutions due to the proposed method is more efficient and accurate method. ................................. ..............................................