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Karbala International Journal of Modern Science
Runge-Kutta method (RK); Runge-Kutta Nystrom method (RKN); Direct method (RKD); RKM; RKT; RKFD; Integrators; Class of seventh-order; Stage; Ordinary differential equations; Order conditions; Taylor expansion.
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Derivation Of Direct Explicit Integrators Of Rk Type For Solving Class Of Seventh-Order Ordinary Differential Equations, Mohammed S. Mechee, Jawad K. Mshachal
Derivation Of Direct Explicit Integrators Of Rk Type For Solving Class Of Seventh-Order Ordinary Differential Equations, Mohammed S. Mechee, Jawad K. Mshachal
Karbala International Journal of Modern Science
The main contribution of this work is the development of direct explicit methods of Runge-Kutta (RK) type for solving class of seventh-order ordinary differential equations (ODEs) to improve computational efficiency. For this purpose, we have generalized RK, RKN, RKD, RKT, RKFD and RKM methods for solving class of first-, second-, third-, fourth-, and fifth-order ODEs. Using Taylor expansion approach, we have derived the algebraic equations of the order conditions for the proposed RKM integrators up to the tenth-order. Based on these order conditions, two RKM methods of fifth- and sixth-order with four- and five-stage are derived. The zero stability of …