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Type :article
Subject :Q Science (General)
Main Author :Annie Gorgey
Additional Authors :Ali J. Kadhim
Title :Extrapolation of GLMs with IRKS property to solve the ordinary differential equations
Place of Production :Tanjong Malim
Publisher :Fakulti Sains dan Matematik
Year of Publication :2019
Corporate Name :Universiti Pendidikan Sultan Idris

Abstract : Universiti Pendidikan Sultan Idris
The extrapolation technique has been proved to be very powerful in improving the performance of the approximate methods by large time whether engineering or scientific problems that are handled on computers. In this paper, we investigate the efficiency of extrapolation of explicit general linear methods with Inherent Runge-Kutta stability in solving the non-stiff problems. The numerical experiments are shown for Van der Pol and Brusselator test problems to determine the efficiency of the explicit general linear methods with extrapolation technique. The numerical results showed that method with extrapolation is efficient than method without extrapolation.

References

[1] Butcher, J.C. (2009) General Linear Methods for Ordinary Differential Equations. Mathematics and Computers in Simulation, 79, 1834-1845. https://doi.org/10.1016/j.matcom.2007.02.006

[2] Wright, W. (2002) General Linear Methods with Inherent Runge-Kutta Stability. Ph.D. Thesis, the University of Auckland, New Zealand.

[3] Bazuaye, F.E. and Osisiogu, U.A. (2017) A New Approach to Constructing Extended Exponential General Linear Methods for Initial Value Problems in Ordinary Differential Equations. International Journal of Advances in Mathematics, 5, 44-54.

[4] Mahdi, H., Abdi, A. and Hojjati, G. (2018) Efficient General Linear Methods for a Class of Volterra Integro-Differential Equations. Applied Numerical Mathematics, 127, 95-109. https://doi.org/10.1016/j.apnum.2018.01.001

[5] Farzi, J. and Mordai, A. (2018) Fuzzy General Linear Methods. arXiv:1812.03394.

[6] Cardone, A., Jackiewicz, Z., Verner J.H. and Welfert, B. (2015) Order Conditions for General Linear Methods. Journal of Computational and Applied Mathematics, 290, 44-64. https://doi.org/10.1016/j.cam.2015.04.042

[7] Butcher, J.C. (2001) General Linear Methods for Stiff Differential Equations. BIT Numerical Mathematics, 41, 240-264. https://doi.org/10.1023/A:1021986222073

[8] Abdi, A. and Jackiewicz, Z. (2019) Towards a Code for Nonstiff Differential Systems Based on General Linear Methods with Inherent Runge-Kutta Stability. Applied Numerical Mathematics, 136, 103-121. https://doi.org/10.1016/j.apnum.2018.10.001

[9] Richardson, L.F. (1911) The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, with an Application to the Stresses in a Masonry Dam. Philosophical Transactions of the Royal Society A, 210, 307-357. https://doi.org/10.1098/rsta.1911.0009

[10] Richardson, L.F. (1927) The Deferred Approach to the Limit. Philosophical Transactions of the Royal Society A, 226, 299-349. https://doi.org/10.1098/rsta.1927.0008

[11] Chan, R.P.K. (1996) A-Stability of Implicit Runge-Kutta Extrapolations. Applied Numerical Mathematics, 22, 179-203. https://doi.org/10.1016/S0168-9274(96)00031-1

[12] Gorgey, A. (2012) Extrapolation of Symmetrized Runge-Kutta Methods. Ph.D. Thesis, the University of Auckland, New Zealand.

[13] Martín-Vaquero, J. and Kleefeld, B. (2016) Extrapolated Stabilized Explicit Runge-Kutta. Methods Journal of Computational Physics, 326, 141-155. https://doi.org/10.1016/j.jcp.2016.08.042

  


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