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A sixth‐order improved Runge–Kutta direct method for special third‐order ordinary differential equations
Author(s) -
Ökten Turacı Mukaddes,
Özdemir Merve
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22562
Subject(s) - runge–kutta methods , mathematics , ordinary differential equation , third order , order (exchange) , l stability , stability (learning theory) , differential equation , mathematical analysis , differential algebraic equation , computer science , finance , machine learning , economics , philosophy , theology
In this paper, we construct a four‐stage explicit improved Runge–Kutta direct (IRKD) method of order six for solving special third‐order ordinary differential equations. The sixth‐order IRKD method is a two‐step method and it requires fewer number of stages compared to the classical Runge–Kutta method of the same order per step. The stability properties of the proposed method are given. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method compared with the existing methods in the literature.