Open AccessThe Scheme of 10th Order Implicit Runge-Kutta Method to Solve the First Order of Initial Value Problems
Author(s) -
Zaiful Bahri,
La Zakaria,
Syamsudhuha Syamsudhuha
Publication year - 2017
Publication title -
insist (international series on integrated science and technology)
Language(s) - English
Resource type - Journals
ISSN - 2502-8588
DOI - 10.23960/ins.v1i1.11
Subject(s) - runge–kutta methods , scheme (mathematics) , ode , mathematics , turbo pascal , computer science , construct (python library) , mathematical optimization , algorithm , numerical analysis , mathematical analysis , programming language
—To construct a scheme of implicit Runge-Kutta methods, there are a number of coefficients that must be determined and satisfying consistency properties and Butcher’s simplifying assumptions. In this paper we provide the numerical simulation technique to obtain a scheme of 10th order Implicit Runge-Kutta (IRK10) method. For simulation process, we construct an algorithm to compute all the coefficients involved in the IRK10 scheme. The algorithm is implemented in a language programming (Turbo Pascal) to obtain all the required coefficients in the scheme. To show that our scheme works correctly, we use the scheme to solve Hénon-Heiles system.Keywords—ODEs, 10th order IRK method, numerical technique, Hénon-Heiles system