Stability and convergence at the PDE/stiff ODE interface

DOI10.1016/0168-9274(89)90028-7zbMath0671.65078OpenAlexW2055070885MaRDI QIDQ1119364

Jesús María Sanz-Serna, Jan G. Verwer

Publication date: 1989

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(89)90028-7

zbMATH Keywords

stabilityevolution equationstiff ordinary differential equationsmethod of linesfully discrete schemeorder reductioncontractivitylogarithmic normsB-convergenceone-sided Lipschitz conditions

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25)

Related Items

Contractivity results for alternating direction schemes in Hilbert spaces, Stability and Convergence of the Peaceman-Rachford ADI Method for Initial-Boundary Value Problems, Galerkin/Runge-Kutta discretizations of nonlinear parabolic equations, Runge-Kutta Methods and Local Uniform Grid Refinement, Convergence properties of the Runge-Kutta-Chebyshev method, Lax-stability of fully discrete spectral methods via stability regions and pseudo-eigenvalues, Stability of schemes for the numerical treatment of an equation modelling fluidized beds, On the Stability of Variable Stepsize Rational Approximations of Holomorphic Semigroups, Stability of linear multistep methods for sectorial operators in Banach spaces, Modern convergence theory for stiff initial-value problems, An easily implementable fourth-order method for the time integration of wave problems, Rosenbrock methods with an explicit first stage, Exponential time integration of solitary waves of cubic Schrödinger equation, Error analysis of multipoint flux domain decomposition methods for evolutionary diffusion problems, Runge-Kutta Methods for Partial Differential Equations and Fractional Orders of Convergence, On error structures and extrapolation for stiff systems, with application in the method of lines, Rational methods with optimal order of convergence for partial differential equations, Spectral/Rosenbrock discretizations without order reduction for linear parabolic problems, Stability of the method of lines

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