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The Magnus Expansion

Hollander R.M. (2017) The Magnus Expansion. Bachelor's Thesis, Mathematics.

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For a homogeneous system of linear differential equations with a constant co- efficient matrix, the fundamental matrix can be computed for example using the Jordan Canonical Form. However, when the coefficient matrix depends on a single variable t, this method does not always provide a correct solution. The fundamental matrix can be computed using a numerical method, for example the Picard itera- tive method, but using such method, one can lose important qualitative properties. Wilhelm Magnus provided a method to approximate the fundamental matrix, such that these qualitative properties are preserved. In this thesis, we will state Magnus’ theorem and it’s proof. We will compute the Magnus Expansion for some simple examples, and compare the solutions with the fundamental matrices obtained by applying Picard iteration.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 08:26
Last Modified: 15 Feb 2018 08:26

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