Optimal convergence results for Runge-Kutta discretizations of linear nonautonomous parabolic problems

DOI10.1023/A:1022369208270zbMath0921.65068MaRDI QIDQ1283249

Cesáreo Ganzález, Alexander Ostermann

Publication date: 25 May 1999

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

convergenceerror boundsBanach spaceRunge-Kutta methodstime-discretizationabstract parabolic equationsparabolic initial-boundary value problemsvariable stepsizestime-dependent smooth coefficients

Mathematics Subject Classification ID

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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25)

Related Items (3)

Magnus-type integrator for non-autonomous SPDEs driven by multiplicative noise ⋮ Design of DIRK schemes with high weak stage order ⋮ Implicit Taylor methods for parabolic problems with nonsmooth data and applications to optimal heat control

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