UPSI Digital Repository (UDRep)
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UPSI Digital Repository (UDRep)
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| Abstract : Universiti Pendidikan Sultan Idris |
| General linear methods have been proven to be very efficient in solving stiff and non-stiff differential equations. Extrapolation is proven to increase the accuracy of any methods. This paper investigates the accuracy and efficiencies of explicit general linear methods with inherent Runge-Kutta stability (IRKs) with and without extrapolation. The numerical results on the Van der Pol (VDP) and Brusselator (Bruss) non-stiff test equations showed that IRKs with extrapolation are more efficient and accurate than itself without extrapolation.
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| References |
Abdi, A., & 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. Bazuaye, F. E., & 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. Butcher, J. C. (2009). General linear methods for ordinary differential equations. Mathematics and Computers in Simulation, 79, 1834–1845. Butcher, J. C. (2016). The numerical analysis of ordinary differential equations: Runge- Kutta and general linear methods. John Wiley and Sons, New York. Farzi, J., & Mordai, A. (2018). Fuzzy general linear methods. arXiv preprint arXiv:1812.03394. Gorgey, A. (2012). Extrapolation of symmetrized Runge-Kutta methods. Ph.D. thesis, The University of Auckland, New Zealand. Hairer, E., Norsett, S. P., & Wanner, G. (1993). Solving Ordinary Differential Equations I. Nonstiff Problems. Springer, Berlin. Ismail, A.,& Gorgey, A. (2012). Efficiency of Extrapolated Runge-Kutta Methods in Solving Linear and Nonlinear Problems. Journal of Science and Mathematics Letters, 1, 1 – 8. Jackiewicz, Z. (2009). General linear methods for ordinary differential equations. John Wiley, Hoboken, New Jersey. Mahdi, H., Abdi, A., & Hojjati, G. (2018). Efficient general linear methods for a class of volterra integrodifferential equations. Applied Numerical Mathematics, 127:95– 109. Richardson, L. F. (1911). The approximate arithmetical solution by finite differences of physical problems involving differential equation, with an application to the stresses in amasonry dam. Philos. Trans. Roy. Soc. London, ser.A, 210, 307– 857. Richardson, L. F. (1927). The deferred approach to the limit. part i. single lattice. part ii. interpenetrating lattices. philosophical transactions of the royal society. Mathematical, Physical and Engineering Sciences, 226, 299–361. Wright, W. (2002). General linear methods with inherent Runge-Kutta stability. Ph.D. thesis, The University of Auckland, New Zealand. Zlatev, Z., Dimov, I., Faragó, I., & Havasi, A. (2018) Richardson extrapolation practical aspects and applications. De Gruyter Series in Applied and Numerical Mathematics
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