A second-order Magnus-type integrator for quasi-linear parabolic problems

DOI10.1090/S0025-5718-06-01883-7zbMath1107.65078OpenAlexW1996761795MaRDI QIDQ3420428

Cesáreo González, Mechthild Thalhammer

Publication date: 2 February 2007

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-06-01883-7

zbMATH Keywords

stabilityconvergenceDirichlet boundary conditionsectorial operatorquasi-linear parabolic problemsMagnus integratorserror estimates in Sobolev spaces

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Abstract parabolic equations (35K90) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stability and convergence of numerical methods for ordinary differential equations (65L20)

Related Items

Geometric integration of non-autonomous linear Hamiltonian problems ⋮ A high-order exponential integrator for nonlinear parabolic equations with nonsmooth initial data ⋮ Exponential Integrators for Quasilinear Wave-Type Equations ⋮ Symmetric-conjugate splitting methods for evolution equations of parabolic type ⋮ Higher-Order Exponential Integrators for Quasi-Linear Parabolic Problems. Part II: Convergence ⋮ Higher-Order Exponential Integrators for Quasi-Linear Parabolic Problems. Part I: Stability

Cites Work

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• The solution of stationary ODE problems in quantum mechanics by Magnus methods with stepsize control
• A second-order Magnus-type integrator for nonautonomous parabolic problems
• Semigroups of linear operators and applications to partial differential equations
• Geometric theory of semilinear parabolic equations
• Improved high order integrators based on the Magnus expansion
• Caractérisation de quelques espaces d'interpolation
• Numerical evaluation of the Evans function by Magnus integration
• Quasilinear Evolution Equations and Parabolic Systems
• Dynamic theory of quasilinear parabolic equations—I. Abstract evolution equations
• On a Nonlinear Elliptic-Parabolic Partial Differential Equation System in a Two-Dimensional Groundwater Flow Problem
• Stability of Runge-Kutta methods for abstract time-dependent parabolic problems: The Hölder case
• Computations in a free Lie algebra
• On the solution of linear differential equations in Lie groups
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• On Magnus Integrators for Time-Dependent Schrödinger Equations
• Non-smooth data error estimates for linearly implicit Runge-Kutta methods
• Stability of Runge-Kutta methods for quasilinear parabolic problems
• Preconditioning Lanczos Approximations to the Matrix Exponential
• On the exponential solution of differential equations for a linear operator
• Analytic semigroups and optimal regularity in parabolic problems