Runge-Kutta time discretizations of nonlinear dissipative evolution equations

DOI10.1090/S0025-5718-05-01866-1zbMath1098.65058MaRDI QIDQ3376987

Eskil Hansen

Publication date: 27 March 2006

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

convergenceCauchy problemHilbert spaceRunge-Kutta methodrankm-dissipative vector field

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (8)

Convergence of the variable two-step BDF time discretisation of nonlinear evolution problems governed by a monotone potential operator ⋮ Galerkin/Runge-Kutta discretizations of nonlinear parabolic equations ⋮ 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 ⋮ Unconditional convergence of DIRK schemes applied to dissipative evolution equations ⋮ 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

Uses Software

• RODAS

Cites Work

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• Stability of linear multistep methods and applications to nonlinear parabolic problems.
• Convergence of Runge-Kutta methods for nonlinear parabolic equations
• Logarithmic norms and nonlinear DAE stability
• Backward Euler discretization of fully nonlinear parabolic problems
• Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems
• Runge-Kutta Methods for Parabolic Equations and Convolution Quadrature
• Runge-Kutta Approximation of Quasi-Linear Parabolic Equations
• Convergence of Multistep Time Discretizations of Nonlinear Dissipative Evolution Equations

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