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arXiv · 1804.02266

Exponential Integrators Preserving Local Conservation Laws of PDEs with Time-Dependent Damping/Driving Forces

Ashish Bhatt·Brian E. Moore
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Abstract

Structure-preserving algorithms for solving conservative PDEs with added linear dissipation are generalized to systems with time-dependent damping/driving terms. This study is motivated by several PDE models of physical phenomena, such as Korteweg-de Vries, Klein-Gordon, Schr\"{o}dinger, and Camassa-Holm equations, all with damping/driving terms and time-dependent coefficients. Since key features of the PDEs under consideration are described by local conservation laws, which are independent of the boundary conditions, the proposed (second-order in time) discretizations are developed with the intent of preserving those local conservation laws. The methods are respectively applied to a damped-driven nonlinear Schr\"{o}dinger equation and a damped Camassa-Holm equation. Numerical experiments illustrate the structure-preserving properties of the methods, as well as favorable results over other competitive schemes.

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Ashish Bhatt, Brian E. Moore. 2018-04-06. Exponential Integrators Preserving Local Conservation Laws of PDEs with Time-Dependent Damping/Driving Forces. https://arxiv.org/abs/1804.02266

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