An Orthogonal Spline Collocation Alternating Direction Implicit Crank--Nicolson Method for Linear Parabolic Problems on Rectangles

DOI10.1137/S0036142997310387zbMath0955.65073OpenAlexW2077636190MaRDI QIDQ4270997

Publication date: 22 November 1999

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0036142997310387

zbMATH Keywords

convergence error bounds implicit method Crank-Nicolson method ADI method orthogonal spline collocation alternating direction linear parabolic initial-boundary problem

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Iterative numerical methods for linear systems (65F10) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Initial value problems for second-order parabolic equations (35K15)

Related Items (14)

High order numerical algorithms based on biquadratic spline collocation for two-dimensional parabolic partial differential equations ⋮ Compact ADI method for solving parabolic differential equations ⋮ Some efficient numerical schemes for approximating the nonlinear two-space dimensional extended Fisher-Kolmogorov equation ⋮ An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems ⋮ Unnamed Item ⋮ A fast ADI orthogonal spline collocation method with graded meshes for the two-dimensional fractional integro-differential equation ⋮ Alternating direction implicit orthogonal spline collocation on some non-rectangular regions with inconsistent partitions ⋮ Orthogonal spline collocation methods for partial differential equations ⋮ A numerical study of mixed parabolic-gradient systems ⋮ ADI spectral collocation methods for parabolic problems ⋮ An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems on evolving domains ⋮ Almost block diagonal linear systems: sequential and parallel solution techniques, and applications ⋮ A heterogeneous alternating-direction method for a micro-macro dilute polymeric fluid model ⋮ ADI-Spectral Collocation Methods for Two-Dimensional Parabolic Equations

Uses Software

COLROW

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