Improved Runge-Kutta direct method with fourth derivative for solving $y'''=f(x,y)$
Authors :
Mukaddes Okten Turac? 1 *
Author Address :
1 Department of Mathematics, Faculty of Arts and Sciences, Pamukkale University, 20160, Denizli, Turkey.
Abstract :
In this study, we derive explicit two-derivative improved Runge-Kutta direct methods (TDIRKD) which incorporates the fourth derivative of the solution to solve special third order ordinary differential equations. The improved Runge-Kutta direct methods are extended to these methods. TDIRKD methods which involve one evaluation of third derivative and multiple evaluations of fourth derivative per step are constructed. Order conditions for TDIRKD methods are derived up to order five. Two-stage fourth-order TDIRKD method is presented. The stability polynomial of the proposed method have been obtained. Numerical computations have been given to illustrate the accuracy and efficiency of the suggested method compared to the accessible methods in the literature.
Keywords :
Special third order ordinary differential equations, RKT method, Order conditions, Runge-Kutta method , IRKD method, RKD method, TDRKT method, Stability Polynomial.
DOI :
Article Info :
Received : January 13, 2021; Accepted : March 13, 2021.
