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2015•Malaysian Journal of ScienceOpen access

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

Kasim Abbas Hussain, Fudziah Bt Ismail, Norazak Senu, Faranak Rabiei, Rabha Waell Ibrahim

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Abstract

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

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What this paper is about

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

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Available abstract

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

Key concepts: Runge–Kutta methods, Ordinary differential equation, Mathematics, Third order, Differential equation, Numerical methods for ordinary differential equations, L-stability, Polynomial

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INTEGRATION FOR SPECIAL THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS USING IMPROVED RUNGE-KUTTA DIRECT METHOD — Research Paper | ScholarLens