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2011•Recent Research in Science and TechnologyOpen access

Implementation of a new third order weighted Runge-Kutta formula based on Centroidal Mean for solving stiff initial value problems

R. Gethsi Sharmila And E. C. Henry Amirtharaj

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Abstract

A new third order weighted Runge-Kutta formula based on Centroidal Mean(CeM) is derived and implemented. To illustrate the effectiveness of the method, a stiff problem has been chosen and compared with the classical fourth order Runge-Kutta method and the third order weighted Runge-Kutta method based on Contraharmonic Mean(CoH). The stability of the new method is analysed. The investigation undertaken in the study reveals that the third order RK method based on CeM suits very well and indicates that this method is superior compared to the other methods discussed for the stiff initial value problems.

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What this paper is about

A new third order weighted Runge-Kutta formula based on Centroidal Mean(CeM) is derived and implemented. To illustrate the effectiveness of the method, a stiff problem has been chosen and compared with the classical fourth order Runge-Kutta method and the third order weighted Runge-Kutta method based on Contraharmonic Mean(CoH). The stability of the new method is analysed. The investigation undertaken in the study reveals that the third order RK method based on CeM suits very well and indicates that this method is superior compared to the other methods discussed for the stiff initial value problems.

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Available abstract

A new third order weighted Runge-Kutta formula based on Centroidal Mean(CeM) is derived and implemented. To illustrate the effectiveness of the method, a stiff problem has been chosen and compared with the classical fourth order Runge-Kutta method and the third order weighted Runge-Kutta method based on Contraharmonic Mean(CoH). The stability of the new method is analysed. The investigation undertaken in the study reveals that the third order RK method based on CeM suits very well and indicates that this method is superior compared to the other methods discussed for the stiff initial value problems.

Key concepts: Runge–Kutta methods, Third order, Mathematics, Applied mathematics, Order (exchange), Stability (learning theory), Initial value problem, Value (mathematics)

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