Modification of Fourth order Runge-Kutta Method for Kutta Form With Geometric Means

Irma Suryani; Roni Roni; Wartono Wartono; Yuslenita Muda

doi:10.15575/kubik.v4i2.6425

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Irma Suryani
UIN Sultan Syarif Kasim Riau
Indonesia

Roni Roni
Indonesia

Wartono Wartono

Yuslenita Muda

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Modification of Fourth order Runge-Kutta Method for Kutta Form With Geometric Means

Irma Suryani^(1*), Roni Roni⁽²⁾, Wartono Wartono⁽³⁾, Yuslenita Muda⁽⁴⁾

(1) UIN Sultan Syarif Kasim Riau, Indonesia
(2) , Indonesia
(3) ,
(4) ,
(*) Corresponding Author

Abstract

This paper discuss how to modified Fourth order Runge-Kutta Kutta method based on the geometric mean. Then we have parameters and however by re-comparing the Taylor series expansion of and up to the 4th order. For make error term re-compering of the Taylor series expansion of and up to the 5th order. In the error term an make substitution for the values of and into the Taylor seriese expansion up to the 5th order. So that we have error term modified Fourth Order Runge-Kutta Kutta based on the geometric mean. Modified Fourth Order Runge-Kutta Kutta based on the geometric mean that usually used to solved ordinary differential equations.

Keywords

Taylor’s series, first order differential equaton, geometric means, Fourth order Runge-Kutta method for Kutta form

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References

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J. G. Zhou, “Lattice Boltzmann methods for shallow water fows”, Penerbit Springer, New York, 2004, p. 20

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DOI: https://doi.org/10.15575/kubik.v4i2.6425

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Modification of Fourth order Runge-Kutta Method for Kutta Form With Geometric Means

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