Open AccessDraining of Water Tank using Runge-Kutta Methods
Author(s) -
Agnes Serawa Anak Jutang*,
Noorhelyna Razali,
Hidayatulfathi Othman,
Hawa Hishamuddin
Publication year - 2020
Publication title -
international journal of recent technology and engineering
Language(s) - English
Resource type - Journals
ISSN - 2277-3878
DOI - 10.35940/ijrte.e5843.018520
Subject(s) - runge–kutta methods , midpoint method , midpoint , euler's formula , euler method , stability (learning theory) , mathematics , differential equation , computer science , set (abstract data type) , mathematical optimization , control theory (sociology) , mathematical analysis , geometry , artificial intelligence , control (management) , machine learning , programming language
The use of water tanks as a tool for storing water before being distributed for daily use has become a widely used system today. Among the attempts to develop a water distribution system is optimization in terms of system and operating costs. In this study, four methods of the Runge Kutta method are the Implicit such as Explicit Euler method, Implicit Euler method, Implicit Midpoint Rule, Runge Kutta Fourth-order method are used and compared with the exact solution method. The method will be compared in terms of accuracy and efficiency in solving differential equations based on set parameters for optimum design of water tank. The accuracy and efficiency of each method can be determined based on error graph. At the end of the study, numerical results obtained indicate that the Implicit Midpoint Rule provides greater stability and accuracy for the fixed stepsize given compared to other numerical methods.