Abstract
The subject of our research is to solve accurately ODEs, which appear in mathematical models arising from several physical processes. For this purpose we develop a new class of weighted iterative operator splitting methods. We present applications to systems of linear ODEs, which might contain also stiff parameters. The benefit of the proposed method is demonstrated with regard to convergence results and comparison to analytical solutions. We provide improved results and convergence rates in comparison with classical operator splitting methods.
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References
Ewing, R.E.: Up-scaling of biological processes and multiphase flow in porous media. IIMA Volumes in Mathematics and its Applications, vol. 295, pp. 195–215. Springer, Heidelberg (2002)
Farago, I., Geiser, J.: Iterative Operator-Splitting Methods for Linear Problems. IJCS, International Journal of Computational Sciences 1(1-3), 64–74 (2005)
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Geiser, J., Kravvaritis, C. (2007). Weighted Iterative Operator-Splitting Methods and Applications. In: Boyanov, T., Dimova, S., Georgiev, K., Nikolov, G. (eds) Numerical Methods and Applications. NMA 2006. Lecture Notes in Computer Science, vol 4310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70942-8_5
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DOI: https://doi.org/10.1007/978-3-540-70942-8_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70940-4
Online ISBN: 978-3-540-70942-8
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