On Solving the Cauchy Problem with Propagators

2014/11/05 by Henrik Stenlund, Stenlund, Henrik
Mathematics · #34A12 #35E15 #35F10 #35F40 #35G10 #35G40 #47D09 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:34A12 #msc:35E15 #msc:35F10 #msc:35F40 #msc:35G10 #msc:35G40 #msc:47D09

paper · pdf · doi:10.48550/arxiv.1411.1402

10 pages

arxiv created 2014/11/05 · arxiv updated 2014/11/07

Abstract

The abstract first order Cauchy problem is solved in terms of Taylor's series leading to a series of operators which is a propagator. It is found that higher order Cauchy problems can be solved in the same way. Since derivatives of order lower than the Cauchy problem are built-in to the problem, it suffices to solve the higher order derivatives in terms of the lower order ones, in a simple way.

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