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

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DOI: 10.4236/am.2016.71002    4,421 Downloads   5,229 Views  Citations

ABSTRACT

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.

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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.

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[1] DEVELOPMENT OF FIFTH-ORDER FIVE-STAGE EXPLICIT ALMOST RUNGE-KUTTA METHODS
Journal of Science, Technology, Mathematics and Education (JOSTMED), 2019

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