A Third Runge Kutta Method Based on a Linear Combination of Arithmetic Mean, Harmonic Mean and Geometric Mean
Applied and Computational Mathematics
Volume 3, Issue 5, October 2014, Pages: 231-234
Received: Jul. 11, 2014;
Accepted: Sep. 12, 2014;
Published: Sep. 30, 2014
Views 2781 Downloads 181
Rini Yanti, Numerical Computing Group, Department of Mathematics, University of Riau, Pekanbaru 28293, Indonesia
M Imran, Numerical Computing Group, Department of Mathematics, University of Riau, Pekanbaru 28293, Indonesia
Syamsudhuha , Numerical Computing Group, Department of Mathematics, University of Riau, Pekanbaru 28293, Indonesia
Follow on us
We present a new third order Runge Kutta method based on linear combination of arithmetic mean, geometric mean and harmonic mean to solve a first order initial value problem. We also derive the local truncation error and show the stability region for the method. Moreover, we compare the new method with Runge Kutta method based on arithmetic mean, geometric mean and harmonic mean. The numerical results show that the performance of the new method is the same as known third order Runge-Kutta methods.
Initial Value Problems, Runge Kutta Method, Arithmetic Mean, Harmonic Mean, Geometric Mean
To cite this article
A Third Runge Kutta Method Based on a Linear Combination of Arithmetic Mean, Harmonic Mean and Geometric Mean, Applied and Computational Mathematics.
Vol. 3, No. 5,
2014, pp. 231-234.
O.Y. Ababneh and R. Rozita, New Third Order Runge Kutta Method Based on Contraharmonic Mean for Stiff Problems, Applied Mathematical Sciences, 3(2009), 365-376.
G. Dahlquist and A. Bjorck, Numerical Method, Prentice-Hall,Inc., New York, 1974.
D.J. Evans, 1989. New Runge-Kutta Methods For Initial Value Problems, Applied Mathematics Letter, 2(1989), pp.25--28.
S.K. Khattri, “Euler's Number and Some Means”, Tamsui Oxford Journal of Information and Mathematical Sciences, 28(2012), pp.369--377.
K.A. Ross, Elementary Analysis, Springer, New York, 1980.
L. P. Shampine, Numerical of Ordinary Diferential Equation, Chapman and Hall, New York, 1994.
A.G. Ujagbe, “On the Stability Analysis of a Geometric Mean 4th Order Runge-Kutta Formula, Mathematical Theory and Modelling, 3(2013), pp.76-91.
A.M. Wazwaz, “A Modified Third Order Runge-Kutta Method”, Applied Mathematics Letter, 3(1990), pp.123-125.