Comparison of numerical methods for solving a system of ordinary differential equations: accuracy, stability and efficiency
2020 (English)Independent thesis Basic level (professional degree), 10 credits / 15 HE credits
Student thesis
Abstract [en]
In this thesis, we compute approximate solutions to initial value problems of first-order linear ODEs using five explicit Runge-Kutta methods, namely the forward Euler method, Heun's method, RK4, RK5, and RK8. This thesis aims to compare the accuracy, stability, and efficiency properties of the five explicit Runge-Kutta methods. For accuracy, we carry out a convergence study to verify the convergence rate of the five explicit Runge-Kutta methods for solving a first-order linear ODE. For stability, we analyze the stability of the five explicit Runge-Kutta methods for solving a linear test equation. For efficiency, we carry out an efficiency study to compare the efficiency of the five explicit Runge-Kutta methods for solving a system of first-order linear ODEs, which is the main focus of this thesis. This system of first-order linear ODEs is a semi-discretization of a two-dimensional wave equation.
Place, publisher, year, edition, pages
2020. , p. 65
Series
LÄRARUTBILDNINGEN
Keywords [en]
Numerical methods, Explicit Runge-Kutta methods, accuracy, stability and efficiency
National Category
Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-48211OAI: oai:DiVA.org:mdh-48211DiVA, id: diva2:1436317
Subject / course
Mathematics/Applied Mathematics
Presentation
2020-06-03, Västerås, 11:00 (English)
Supervisors
Examiners
2020-06-092020-06-072020-06-09Bibliographically approved