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
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Authors
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
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Abstract
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.
Keywords
Initial Value Problems, Runge Kutta Method, Arithmetic Mean, Harmonic Mean, Geometric Mean
To cite this article
Rini Yanti, M Imran, Syamsudhuha , 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. doi: 10.11648/j.acm.20140305.16
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