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A 2-Stage Implicit Runge-Kutta Method Based on Heronian Mean for Solving Ordinary Differential Equations
Pure and Applied Mathematics Journal
Volume 9, Issue 5, October 2020, Pages: 84-90
Received: Jul. 23, 2020; Accepted: Aug. 17, 2020; Published: Sep. 8, 2020
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Adegoke Stephen Olaniyan, Department of Mathematics, Lagos State University, Lagos, Nigeria
Omolara Fatimah Bakre, Department of Mathematics, Federal College of Education (Technical), Lagos, Nigeria
Moses Adebowale Akanbi, Department of Mathematics, Lagos State University, Lagos, Nigeria
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In recent times, the use of different types of mean in the derivation of explicit Runge-Kutta methods had been on increase. Researchers have explored explicit Runge-Kutta methods derivation by using different types of mean such as geometric mean, harmonic mean, contra-harmonic mean, heronian mean to name but a few; as against the conventional explicit Runge-Kutta methods which was viewed as arithmetic mean. However, despite efforts to improve the derivation of explicit Runge-Kutta methods with use of other types of mean, none has deemed it fit to extend this notion to implicit Runge-Kutta methods. In this article, we present the use of heronian mean as a basis for the construction of implicit Runge-Kutta method in a way of improving the conventional method which is arithmetic mean based. Numerical results was conducted on ordinary differential equations which was compared with the conventional two-stage fourth order implicit Runge-Kutta (IRK4) method and two-stage third order diagonally implicit Runge-Kutta (DIRK3) method. The results presented confirmed that the new scheme performs better than these numerical methods. A better Qualitative properties using Dalquist test equation were established.
Implicit Runge-Kutta, Heronian Mean, Absolute Stability, Convergence, Ordinary Differential Equation
To cite this article
Adegoke Stephen Olaniyan, Omolara Fatimah Bakre, Moses Adebowale Akanbi, A 2-Stage Implicit Runge-Kutta Method Based on Heronian Mean for Solving Ordinary Differential Equations, Pure and Applied Mathematics Journal. Vol. 9, No. 5, 2020, pp. 84-90. doi: 10.11648/j.pamj.20200905.11
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This article 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.
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