APLIKASI ROOTED TREES PADA METODE RUNGE-KUTTA

• Main Authors: , TRI KUNCORO PRASETYO HUTOMO, , Dr. Sumardi, M.Si.
• Format: Theses and Dissertations NonPeerReviewed
• Published: [Yogyakarta] : Universitas Gadjah Mada 2014
• Subjects: ETD
• Online Access: https://repository.ugm.ac.id/131506/; http://etd.ugm.ac.id/index.php?mod=penelitian_detail&sub=PenelitianDetail&act=view&typ=html&buku_id=72002
• Institution: Universitas Gadjah Mada

Runge-Kutta is a method to estimate the exact value of a differential equation with initial value. This method basically has a general equation containing constants with unknown value. We can find the value of these constants by expand a general equation of Runge-Kutta method with Taylor expansion and is equated by Taylor expansion of the exact solution of a differential equation. However, the Taylor expansions would be cumbersome performed when it reaches a high level derivative. Therefore, both Taylor expansion of Runge-Kutta method�s general equation and Taylor expansion of exact solution of a differential equation need to be connected with the labeling on rooted trees. So, we can find the value of the constants of Runge-Kutta method simply by applying the labeling.