Abstract
The main contribution of this work is the development of direct explicit methods of RK-type for solving class of eighth-order ordinary differential equations (ODEs) to improve the computational efficiency of the methods. For this purpose, we have generalized RK, RKN, RKD, RKT, RKFD and RKM methods for solving class of rst-, second-, third-, fourth-, fth-, sixth- and seventh-orders ODEs. Using Taylor-expansion approach, we have derived the algebraic equations of the order-conditions for the proposed RKM integrators. Based on these order-conditions, proposed method of eighth-order with ve-stage has been derived. The zero stability of the method is proven. Stability polynomial of the method for linear special eighth-order ODE is given. Numerical results have clearly shown the advantage and the efficiency of the new method and agree well with analytical solutions due to the fact that the proposed integrators are zero stable, more efficient and accurate integrators.