A high-order global spatially adaptive collocation method for 1-D parabolic PDEs

DOI10.1016/j.apnum.2003.12.023zbMath1049.65110OpenAlexW2010129860MaRDI QIDQ596575

Rong Wang, Patrick Keast, P. H. Muir

Publication date: 10 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2003.12.023

zbMATH Keywords

algorithmnumerical exampleserror estimateB-splines1-D parabolic PDEsCollocationEquidistribution principleHigh-orderMesh selection

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) 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) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items

High order numerical algorithms based on biquadratic spline collocation for two-dimensional parabolic partial differential equations, A comparison of adaptive software for 1D parabolic PDEs, Extending BACOLI to Solve the Monodomain Model, An Analysis of the Reliability of Error Control B-Spline Gaussian Collocation PDE Software, Performance analysis of error-control B-spline Gaussian collocation software for PDEs, The impact of parameter selection on the performance of an automatic adaptive code for solving reaction-diffusion equations in three dimensions, Quadratic spline collocation for one-dimensional linear parabolic partial differential equations, A posteriori error estimation for $hp$-adaptivity for fourth-order equations, An adaptive mesh method for 1D hyperbolic conservation laws, Error control Gaussian collocation software for boundary value ODEs and 1D time-dependent PDEs

Uses Software

• EPDCOL
• PDECOL
• DASSL
• MOVCOL
• COLROW
• COLSYS
• Algorithm 731
• CWRESU
• CWRESX
• ARCELO

Cites Work

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• On simple moving grid methods for one-dimensional evolutionary partial differential equations
• A practical guide to splines
• A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems
• On spatial adaptivity and interpolation when using the method of lines
• A composite integration scheme for the numerical solution of systems of parabolic PDEs in one space dimension
• Comparison of adaptive methods for one-dimensional parabolic systems
• A moving collocation method for solving time dependent partial differential equations
• FORTRAN Packages for Solving Certain Almost Block Diagonal Linear Systems by Modified Alternate Row and Column Elimination
• Moving Finite Elements. I
• Algorithm 540: PDECOL, General Collocation Software for Partial Differential Equations [D3]
• Collocation Software for Boundary-Value ODEs
• Package for Calculating with B-Splines
• A Posteriori Error Estimation with Finite Element Semi- and Fully Discrete Methods for Nonlinear Parabolic Equations in One Space Dimension
• Algorithm 731: A moving-grid interface for systems of one-dimensional time-dependent partial differential equations
• Algorithm 688: EPDCOL
• High-Order Finite Element Methods for Singularly Perturbed Elliptic and Parabolic Problems
• BACOL
• Interpolation error-based a posteriori error estimation for two-point boundary value problems and parabolic equations in one space dimension