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Conservative discretizations and long-term stability

Abstract:

Conservative discretizations are numerical methods which preserve conservation laws of differential equations at the discrete level. Recently, the multiplier method was proposed as a conservative discretization for general ODEs and PDEs. In contrast to symplectic or variational methods, the multiplier method is applicable even for systems without a symplectic or variational structure, such as dissipative problems. In this talk, I will introduce the multiplier method and discuss some recent results on long-term stability of conservative discretizations.聽