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Numerical methods for solving large-scale systems of differential equations

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Abstract

In this paper, we propose two new methods to solve large-scale systems of differential equations, which are based on the Krylov method. In the first one, the exact solution with the exponential projection technique of the matrix. In the second, we get a new problem of small size, by dropping the initial problem, and then we solve it in ways, such as the Rosenbrock and the BDF. Some theoretical results are presented such as an accurate expression of the remaining criteria. We give an expression of error report and numerical values to compare the two methods in terms of how long each method takes, and we also compare the approaches.

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Acknowledgements

The authors should express their deep-felt thanks to the anonymous referees for their encouraging and constructive comments, which improved this paper.

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  1. Faculty of Sciences, Chouaib Doukkali University, El Jadida, Morocco

    Lakhlifa Sadek & Hamad Talibi Alaoui

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  1. Lakhlifa Sadek
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  2. Hamad Talibi Alaoui
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Correspondence to Lakhlifa Sadek.

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Sadek, L., Talibi Alaoui, H. Numerical methods for solving large-scale systems of differential equations. Ricerche mat 72, 785–802 (2023). https://doi.org/10.1007/s11587-021-00585-1

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