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New third order Runge Kutta based on contraharmonic mean for stiff problems. (English) Zbl 1176.65079
Summary: We introduce an explicit one-step method that can be used for solving stiff problems. This method can be viewed as a modification of the explicit third order Runge-Kutta method using the contraharmonic mean ($$C_oM$$) that allows reducing the stiffness in some sense. The stability of the method is analyzed and numerical results are shown to verify the conclusions. Numerical examples indicate that this method is superior compared to some existing methods including the third and fourth order contraharmonic mean methods, Adams-Bashforth-Moulton method, the classical third order Runge-Kutta method, and the Wazwaz method [A. M. Wazwaz, Appl. Math. Lett. 3, No. 3, 123–125 (1990; Zbl 0705.65056)].

MSC:
 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 62J05 Linear regression; mixed models 70F99 Dynamics of a system of particles, including celestial mechanics
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