2023/10/02 by Karolina Kropielnicka, Kropielnicka, Karolina, J. C. del Valle +1 · 1 citation
Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #G.1.7 #G.1.8 #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2310.01556
openalex publication_date 2023/10/02 · openalex created_date 2023/10/05 · openalex updated_date 2026/07/28
For linear differential equations of the form u'(t)=[A + B(t)] u(t), t≥0, with a possibly unbounded operator A, we construct and deduce error bounds for two families of second-order exponential splittings. The role of quadratures when integrating the twice-iterated Duhamel's formula is reformulated: we show that their choice defines the structure of the splitting. Furthermore, the reformulation allows us to consider quadratures based on the Birkhoff interpolation to obtain not only pure-stages splittings but also those containing derivatives of B(t) and commutators of A and B(t). In this approach, the construction and error analysis of the splittings are carried out simultaneously. We discuss the accuracy of the members of the families. Numerical experiments are presented to complement the theoretical consideration.