INTEGRATION FOR SPECIAL THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS USING IMPROVED RUNGE-KUTTA DIRECT METHOD

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Kasim Abbas Hussain Fudziah Ismail Norazak Senu Faranak Rabiei Rabha Ibrahim

Abstract

In this paper, we derive an explicit four stage fifth-order Improved Runge-Kutta (IRKD) method
for numerical integration of special third-order ordinary differential equation. The method proposed here is two-step
in nature and require less number of stages per step compared with the existing Runge-Kutta (RK) method. The
stability polynomial of the IRKD method is presented. Numerical results are given to illustrate the efficiency of the
proposed method compared to the RK method and direct Runge-Kutta (RKD) method for solving special third-order
ordinary differential equations.


Keywords: Special third-order ordinary differential equations, Runge-Kutta method, IRKD method, Stability
Ploynomial

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How to Cite
HUSSAIN, Kasim Abbas et al. INTEGRATION FOR SPECIAL THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS USING IMPROVED RUNGE-KUTTA DIRECT METHOD. MJS, [S.l.], v. 34, n. 2, p. 172-179, dec. 2015. ISSN 2600-8688. Available at: <https://mjs.um.edu.my/article/view/6563>. Date accessed: 18 mar. 2019. doi: https://doi.org/10.22452/mjs.vol34no2.4.
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