An optimized finite difference Crank-Nicolson iterative scheme for the 2D Sobolev equation

DOI10.1186/s13662-017-1253-8zbMath1422.65191OpenAlexW2735849638WikidataQ59524791 ScholiaQ59524791MaRDI QIDQ1631955

Hong Xia, Zhen-Dong Luo

Publication date: 7 December 2018

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-017-1253-8

zbMATH Keywords

proper orthogonal decompositionnumerical simulationSobolev equationstability and convergenceCrank-Nicolson iterative scheme

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Initial-boundary value problems for second-order parabolic equations (35K20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

Related Items (5)

The reduced-dimension technique for the unknown solution coefficient vectors in the Crank-Nicolson finite element method for the Sobolev equation ⋮ A space-time spectral method for multi-dimensional Sobolev equations ⋮ A reduced‐order extrapolating space–time continuous finite element method for the 2D Sobolev equation ⋮ A reduced-order extrapolated finite difference iterative scheme for uniform transmission line equation ⋮ One-parameter orthogonal spline collocation methods for nonlinear two-dimensional Sobolev equations with time-variable delay

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