Improved Runge-Kutta direct method with fourth derivative for solving $y^{\prime \prime \prime}=f(x, y)$
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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 PolynomialMathematics Subject Classification:
Mathematics- Pages: 864-869
- Date Published: 01-01-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
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