Discrete Variational Methods and Symplectic Generalized Additive\n Runge--Kutta Methods

2020/01/20 by Antonella Zanna, Zanna, Antonella
Computer Science · Engineering · Mathematics · #37J05 #65L06 #70H15 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2001.07185

openalex publication_date 2020/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a Lagrangian system L(q, q) =\n \∑_l=1^NL^ l (q, q), where the q-variable is treated by a\nGeneralized Additive Runge--Kutta (GARK) method. Applying the technique of\ndiscrete variations, we show how to construct symplectic schemes. Assuming the\ndiagonal methods for the GARK given, we present some techinques for\nconstructing the transition matrices. We address the problem of the order of\nthe methods and discuss some semi-separable and separable problems, showing\nsome interesting constructions of methods with non-square coefficient matrices.\n

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