Convergence of Multistep Time Discretizations of Nonlinear Dissipative Evolution Equations

DOI10.1137/040610362zbMath1118.65055OpenAlexW1964299890MaRDI QIDQ5470946

Eskil Hansen

Publication date: 2 June 2006

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/040610362

zbMATH Keywords

stabilityconvergenceconsistencysemigroupToeplitz matrixnonlinear evolution equationmultistep methodlogarithmic Lipschitz constantglobal error analysisdissipative mapevolution mapBanach/Hilbert spaceimpliciteness

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) Nonlinear differential equations in abstract spaces (34G20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (10)

Entropy dissipative one‐leg multistep time approximations of nonlinear diffusive equations ⋮ Convergence of the variable two-step BDF time discretisation of nonlinear evolution problems governed by a monotone potential operator ⋮ Stability and Convergence of Stepsize-Dependent Linear Multistep Methods for Nonlinear Dissipative Evolution Equations in Banach Space ⋮ The logarithmic norm. History and modern theory ⋮ Time discretisation of monotone nonlinear evolution problems by the discontinuous Galerkin method ⋮ Observations on evolutionary models with (or without) time lag, and on problematical paradigms ⋮ Stiffly accurate Runge–Kutta methods for nonlinear evolution problems governed by a monotone operator ⋮ Variable time-step \(\vartheta\)-scheme for nonlinear evolution equations governed by a monotone operator ⋮ Runge-Kutta time discretizations of nonlinear dissipative evolution equations ⋮ A variational formulation of the BDF2 method for metric gradient flows

This page was built for publication: Convergence of Multistep Time Discretizations of Nonlinear Dissipative Evolution Equations