Please use this identifier to cite or link to this item: http://repo.lib.jfn.ac.lk/ujrr/handle/123456789/3807
Title: A class of s-step non-linear iteration scheme based on projection method for gauss method.
Authors: Vigneswaran, R.
Kajanthan, S.
Keywords: Gauss method;Implementation;Projection method;Rate of convergence;Stiff systems
Issue Date: 2019
Publisher: Knowve; publishers
Citation: R. Vigneswaran and S.Kajanthan, “A Class of s-step Non-linear Iteration Scheme Based On Projection Method For Gauss Method”, Advances in Mathematical Sciences, vol.2, pp.26–30, 2019. https://doi.org/10.37516/adv.math.sci.2019.0061.
Abstract: Various iteration schemes are proposed by various authors to solve non-linear equations arising in the implementation of implicit Runge-Kutta methods. In this paper, a class of s-step non-linear scheme based on projection method is proposed to accelerate the convergence rate of those linear iteration schemes. In this scheme, sequence of numerical solutions is updated after each sub-step is completed. For 2-stage Gauss method, upper bound for the spectral radius of its iteration matrix was obtained in the left half complex plane. This result is extended to 3-stage and 4-stage Gauss methods by transforming the coefficient matrix and the iteration matrix to a block diagonal form. Finally, some numerical experiments are carried out to confirm the obtained theoretical results.
URI: http://repo.lib.jfn.ac.lk/ujrr/handle/123456789/3807
Appears in Collections:Interdisciplinary Studies FoT

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