Applied Mathematics

Volume 7, Issue 1 (January 2016)

ISSN Print: 2152-7385   ISSN Online: 2152-7393

Google-based Impact Factor: 0.83  Citations  

Design and Analysis of Some Third Order Explicit Almost Runge-Kutta Methods

HTML  XML Download Download as PDF (Size: 399KB)  PP. 13-21  
DOI: 10.4236/am.2016.71002    4,421 Downloads   5,229 Views  Citations


In this paper, we propose two new explicit Almost Runge-Kutta (ARK) methods, ARK3 (a three stage third order method, i.e., s = p = 3) and ARK34 (a four-stage third-order method, i.e., s = 4, p = 3), for the numerical solution of initial value problems (IVPs). The methods are derived through the application of order and stability conditions normally associated with Runge-Kutta methods; the derived methods are further tested for consistency and stability, a necessary requirement for convergence of any numerical scheme; they are shown to satisfy the criteria for both consistency and stability; hence their convergence is guaranteed. Numerical experiments carried out further justified the efficiency of the methods.

Share and Cite:

Ndanusa, A. and Audu, K. (2016) Design and Analysis of Some Third Order Explicit Almost Runge-Kutta Methods. Applied Mathematics, 7, 13-21. doi: 10.4236/am.2016.71002.

Cited by

Journal of Science, Technology, Mathematics and Education (JOSTMED), 2019

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.