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http://repo.lib.jfn.ac.lk/ujrr/handle/123456789/3808
Title: | Some efficient implementation schemes for implicit RUNGE-KUTTA methods |
Authors: | Vigneswaran, R. Kajanthan, S. |
Keywords: | Implementation;Gauss methods;Rate of convergence;Stiff sys- tems |
Issue Date: | 2014 |
Publisher: | Academic Publications, Ltd |
Citation: | : R.Vigneswaran and S.Kajanthan, “Some Efficient Implementation Schemes for Implicit Runge- Kutta Methods”, International Journal of Pure and Applied Mathematics (IJPAM), vol.93, no.4, pp.525–540, 2014. https://doi.org/10.12732/ijpam.v93i4.4. |
Abstract: | Several iteration schemes have been proposed to solve the nonlinear equations arising in the implementation of implicit Runge-Kutta methods. As an alternative to the modified Newton scheme, some iteration schemes with reduced linear algebra costs have been proposed A scheme of this type proposed in [9] avoids expensive vector transformations and is computationally more efficient. The rate of convergence of this scheme is examined in [9] when it is applied to the scalar test differential equation x ′ = qx and the convergence rate depends on the spectral radius of the iteration matrix M(z), a function of z = hq, where h is the step-length. In this scheme, we require the spectral radius of M(z) to be zero at z = 0 and at z = ∞ in the z-plane in order to improve the rate of convergence of the scheme. New schemes with parameters are obtained for three-stage and four-stage Gauss methods. Numerical experiments are carried out to confirm the results obtained here. |
URI: | http://repo.lib.jfn.ac.lk/ujrr/handle/123456789/3808 |
Appears in Collections: | Interdisciplinary Studies FoT |
Files in This Item:
File | Description | Size | Format | |
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SOME EFFICIENT IMPLEMENTATION SCHEMES.pdf | 161.06 kB | Adobe PDF | View/Open |
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