First order linear ordinary differential equations in associative algebras
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In this paper, we study the linear differential equation dx / dt = nΣ i=1 ai(t)xbi(t) + f(t) in an associative but non-commutative algebra A, where the bi(t) form a set of commuting A-valued functions expressed in a time-independent spectral basis consisting of mutually annihilating idempotents and nilpotents. Explicit new closed solutions are derived, and examples are presented to illustrate the theory.
CitationErlebacher, G., & Sobczyk, G. E. (2004). First order linear ordinary differential equations in associative algebras. Electronic Journal of Differential Equations, 2004(1), pp. 1-18.
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