Validating Explicit Third Order Euler Technique for Reactor Design and Exponential Growth Problems
Keywords:Exponential growth, reactor design, explicit third order Euler method, ordinary differential equations, initial value problems
The purpose of this present paper is to validate an explicit third order Euler approximation technique for reactor design and exponential growth problems. The computation results reveal that the numerical solution obtained by explicit third order Euler method is better in comparison with analytical solution due to simple improvement carried out in the employed method. The advantage of employing explicit third order Euler method is consistent, stable, efficient, accurate, convergent order is 3, wider region of absolute stability and easy to implement with lower computational cost.
H Euler. Institutiones Calculi Integralis. Vol XI, Volumen Primum, Opera Omnia, BG Teubneri Lipsiae et Berolini MCMXIII, 1768.
L Euler. De Integratione Aequationum di Erentialium per Approximationem. Vol 11. In Opera Omnia, Institutiones Calculi Integralis, Teubner, Leipzig and Berlin, 1913, p. 424-34.
C Runge. Ueber die numerische Auflösung von differentialgleichungen. Math. Ann. 1895; 46, 167-78.
MA Akanbi. Third order Euler method for numerical solution of ordinary differential equations. ARPN J. Eng. Appl. Sci. 2010; 5, 42-49.
S Senthilkumar. 2009, New Embedded Runge-Kutta Fourth Order Four Stage Algorithms for Raster and Time-Multiplexing Cellular Neural Networks Simulation. Ph.D. Thesis, Department of Mathematics, National Institute of Technology, Tiruchirappalli, Tamilnadu, India.
JC Butcher and G Wanner. Ruge-Kutta methods: Some historical notes. Appl. Numer. Math. 1996; 22, 113-51.
EHC Julyan and O Piro. The dynamics of Runge-Kutta methods, Int. J. Bifurcat. Chaos 1995; 2, 427-49.
UM Ascher and LR Petzold. Computer Methods for Ordinary Differential Equations and Differential - Algebraic Equations. Society for Industrial and Applied Mathematics, Philadelphia, 1998.
TE Hull, WH Enright, BM Fellen and AE Sedgwick. Comparing numerical methods for ordinary differential equations. SIAM J. Numer. Anal. 1972; 9, 603-37.
SO Fatunla. Numerical Methods for Initial Value Problems in Ordinary Differential Equations. Academy Press, London, USA, 1988.
EA Kendall. An Introduction to Numerical Analysis. 2nd ed. John Wiley and Sons, 1989.
JD Lambert. Numerical Methods for Ordinary Differential Equations. John Wiley and Sons, 1991.
JD Lambert. Numerical Methods for Ordinary Differential Systems: The Initial Value Problem. John Wiley & Sons, 1991.
JD Lambert. Computational Methods in ODEs. John Wiley & Sons, 1973.
JC Butcher. A history of Runge-Kutta methods. Appl. Numer. Math. 1996; 20, 247-60.
IK Adewale. 1998, A New Five-Stage Runge-Kutta Method for Initial Value Problems. M. Tech. Dissertation, Federal University of Technology, Minna, Nigeria.
JC Butcher. General linear methods: A survey. Appl. Numer. Math. 1985; 1, 273-84.
JHJ Lee. 2004, Numerical Methods for Ordinary Differential Systems: A Survey of Some Standard Methods. M. Sc. Thesis, University of Auckland, Auckland, New Zealand.
W Kutta. Beitrag Zur naherungsweisen integration totaler differentialgleichungen. Zeitschr. Math. Phys. 1901; 46, 435-53.
How to Cite
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.