Next Article in Journal
Facial Expression Recognition Based on Discrete Separable Shearlet Transform and Feature Selection
Previous Article in Journal
Comparative Study in Fuzzy Controller Optimization Using Bee Colony, Differential Evolution, and Harmony Search Algorithms
Article Menu

Export Article

Open AccessArticle
Algorithms 2019, 12(1), 10; https://doi.org/10.3390/a12010010

Diagonally Implicit Runge–Kutta Type Method for Directly Solving Special Fourth-Order Ordinary Differential Equations with Ill-Posed Problem of a Beam on Elastic Foundation

1
Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia
2
Department of Mathematics, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia
3
Department of Mathematics, Faculty of Computer Science and Mathematics, University of Tikrit, Tikrit P.O. Box 42, Iraq
*
Author to whom correspondence should be addressed.
Received: 7 December 2018 / Revised: 24 December 2018 / Accepted: 27 December 2018 / Published: 29 December 2018
Full-Text   |   PDF [745 KB, uploaded 29 December 2018]   |  
  |   Review Reports

Abstract

In this study, fifth-order and sixth-order diagonally implicit Runge–Kutta type (DIRKT) techniques for solving fourth-order ordinary differential equations (ODEs) are derived which are denoted as DIRKT5 and DIRKT6, respectively. The first method has three and the another one has four identical nonzero diagonal elements. A set of test problems are applied to validate the methods and numerical results showed that the proposed methods are more efficient in terms of accuracy and number of function evaluations compared to the existing implicit Runge–Kutta (RK) methods. View Full-Text
Keywords: diagonally implicit Runge–Kutta type methods; fourth-order ODEs; initial value problem diagonally implicit Runge–Kutta type methods; fourth-order ODEs; initial value problem
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Ghawadri, N.; Senu, N.; Adel Fawzi, F.; Ismail, F.; Ibrahim, Z.B. Diagonally Implicit Runge–Kutta Type Method for Directly Solving Special Fourth-Order Ordinary Differential Equations with Ill-Posed Problem of a Beam on Elastic Foundation. Algorithms 2019, 12, 10.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Algorithms EISSN 1999-4893 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top