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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 |
Files in This Item:
File | Description | Size | Format | |
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A CLASS OF S-STEP NON-LINEAR ITERATION SCHEME BASED ON.pdf | 760.59 kB | Adobe PDF | View/Open |
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