Strang Splitting Method for Semilinear Parabolic Problems With Inhomogeneous Boundary Conditions: A Correction Based on the Flow of the Nonlinearity

DOI10.1137/19M1257081zbMath1447.65058arXiv1904.08826OpenAlexW3039896695MaRDI QIDQ3300862

Guillaume Bertoli, Gilles Vilmart

Publication date: 30 July 2020

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.08826

zbMATH Keywords

nonhomogeneous boundary conditionsdiffusion-reaction equationorder reductionStrang splittingstiff nonlinearity

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Semilinear parabolic equations (35K58) Numerical methods for stiff equations (65L04)

Related Items (4)

Symmetric-conjugate splitting methods for evolution equations of parabolic type ⋮ Geometric numerical integration. Abstracts from the workshop held March 28 -- April 3, 2021 (hybrid meeting) ⋮ Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with Dirichlet and oblique boundary conditions ⋮ A modified Gautschi's method without order reduction when integrating boundary value nonlinear wave problems

Uses Software

• Algorithm 919
• phipm

Cites Work

• Solving parabolic integro-differential equations by an explicit integration method
• Error bounds for exponential operator splittings
• Efficient boundary corrected Strang splitting
• Caractérisation de quelques espaces d'interpolation
• Overcoming Order Reduction in Diffusion-Reaction Splitting. Part 2: Oblique Boundary Conditions
• Algorithm 919
• Geometric Numerical Integration
• Overcoming Order Reduction in Diffusion-Reaction Splitting. Part 1: Dirichlet Boundary Conditions
• Concrete characterization of the domains of fractional powers of some elliptic differential operators of the second order
• Analytic semigroups and optimal regularity in parabolic problems

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