Computation of higher order Lie derivatives on the Infinity Computer

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:383

Article

Iavernaro, F.¹  Mazzia, F.²  Mukhametzhanov, M. S.^3,4  Sergeyev, Ya D.^3,4 

[1] Univ Bari Aldo Moro, Dipartimento Matemat, Bari, BA, Italy

[2] Univ Bari Aldo Moro, Dipartimento Informat, Bari, BA, Italy

[3] Univ Calabria, DIMES, Calabria, Italy

[4] Lobachevsky State Univ Nizhni Novgorod, IITMM, Nizhnii Novgorod, Nizhny Novgorod, Russia

关键词: Lie derivatives;    Ordinary differential equations;    Multi-derivative methods;    Derivatives computation;    Numerical infinitesimals;    Infinity computer;   

DOI  :  10.1016/j.cam.2020.113135

来源: Elsevier

【 摘 要 】

In this paper, we deal with the computation of Lie derivatives, which are required, for example, in some numerical methods for the solution of differential equations. One common way for computing them is to use symbolic computation. Computer algebra software, however, might fail if the function is complicated, and cannot be even performed if an explicit formulation of the function is not available, but we have only an algorithm for its computation. An alternative way to address the problem is to use automatic differentiation. In this case, we only need the implementation of the algorithm that evaluates the function in terms of its analytic expression in a programming language, but we cannot use this if we have only a compiled version of the function. In this paper, we present a novel approach for calculating the Lie derivative of a function, even in the case where its analytical expression is not available, that is based on the Infinity Computer arithmetic. A comparison with symbolic and automatic differentiation shows the potentiality of the proposed technique. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free