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Mathematics > Numerical Analysis

arXiv:2003.09789 (math)
[Submitted on 22 Mar 2020 (v1), last revised 6 Apr 2020 (this version, v2)]

Title:Generalization of partitioned Runge--Kutta methods for adjoint systems

Authors:Takeru Matsuda, Yuto Miyatake
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Abstract:This study computes the gradient of a function of numerical solutions of ordinary differential equations (ODEs) with respect to the initial condition. The adjoint method computes the gradient approximately by solving the corresponding adjoint system numerically. In this context, Sanz-Serna [SIAM Rev., 58 (2016), pp. 3--33] showed that when the initial value problem is solved by a Runge--Kutta (RK) method, the gradient can be exactly computed by applying an appropriate RK method to the adjoint system. Focusing on the case where the initial value problem is solved by a partitioned RK (PRK) method, this paper presents a numerical method, which can be seen as a generalization of PRK methods, for the adjoint system that gives the exact gradient.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2003.09789 [math.NA]
  (or arXiv:2003.09789v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2003.09789

Submission history

From: Yuto Miyatake [view email]
[v1] Sun, 22 Mar 2020 02:58:45 UTC (15 KB)
[v2] Mon, 6 Apr 2020 06:03:36 UTC (15 KB)
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