Analysis of Runge-Kutta methods using Butcher tableaus
C.M.E. Kauppinen (TU Delft - Electrical Engineering, Mathematics and Computer Science)
D. den Ouden-van der Horst – Mentor (TU Delft - Numerical Analysis)
C. Kraaikamp – Graduation committee member (TU Delft - Applied Probability)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
This Bachelor thesis provides an analysis of Runge-Kutta methods using Butcher tableaus. Runge-Kutta method are numerical methods used for approximating initial value problems. A Runge-Kutta method can be classified as either an explicit or an implicit method. A special kind of implicit methods are diagonally implicit methods. The type of method can be recognised by the Butcher tableau.
Using the entries of the Butcher tableau, one can compute the amplification factor of a Runge-Kutta method. The amplification factor can then be used to compute the order of the local truncation error and the stability region. Examples of these computations are given for seven methods. Furthermore, this thesis provides an algorithm to perform time steps for each of the three types of Runge-Kutta methods. Finally, in order to analyse the global truncation error of the seven methods, the algorithm to perform time steps is used with different step sizes.