Stability of Runge-Kutta methods for quasilinear parabolic problems

DOI10.1090/S0025-5718-99-01156-4zbMath0941.65098OpenAlexW2045723852MaRDI QIDQ4942780

Cesáreo González, César Palencia

Publication date: 15 March 2000

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-99-01156-4

zbMATH Keywords

stabilityconvergenceBanach spacesemidiscretizationRunge-Kutta methodsquasilinear parabolic problems

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Nonlinear differential equations in abstract spaces (34G20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) 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) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items

A class of explicit multistep exponential integrators for semilinear problems, Convergence of the variable two-step BDF time discretisation of nonlinear evolution problems governed by a monotone potential operator, Time discretisation of monotone nonlinear evolution problems by the discontinuous Galerkin method, Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type, Backward Euler discretization of fully nonlinear parabolic problems, Stiffly accurate Runge–Kutta methods for nonlinear evolution problems governed by a monotone operator, \(A\)-stable Runge-Kutta methods for semilinear evolution equations, Variable time-step \(\vartheta\)-scheme for nonlinear evolution equations governed by a monotone operator, On variable stepsize Runge-Kutta approximations of a Cauchy problem for the evolution equation, A second-order Magnus-type integrator for quasi-linear parabolic problems, Stability of Runge-Kutta methods for abstract time-dependent parabolic problems: The Hölder case

Uses Software

• RODAS

Cites Work

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