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math.NA2022
High-order linearly implicit schemes conserving quadratic invariants
Shun Sato, Yuto Miyatake, John C. Butcher
In this paper, we propose linearly implicit and arbitrary high-order conservative numerical schemes for ordinary differential equations with a quadratic invariant. Many differentia…
math.NA2021
Scalar auxiliary variable approach for conservative/dissipative partial differential equations with unbounded energy
Tomoya Kemmochi, Shun Sato
In this paper, we present a novel investigation of the so-called SAV approach, which is a framework to construct linearly implicit geometric numerical integrators for partial diffe…
math.NA2019
Linearly implicit structure-preserving schemes for Hamiltonian systems
Sølve Eidnes, Lu Li, Shun Sato
Kahan's method and a two-step generalization of the discrete gradient method are both linearly implicit methods that can preserve a modified energy for Hamiltonian systems with a c…