An invariant moving mesh scheme for the nonlinear diffusion equation

DOI10.1016/S0168-9274(97)00079-2zbMath0911.65081OpenAlexW1988083967WikidataQ127633872 ScholiaQ127633872MaRDI QIDQ1379053

G. J. Collins, Chris J. Budd

Publication date: 26 April 1999

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

Full work available at URL: https://doi.org/10.1016/s0168-9274(97)00079-2

zbMATH Keywords

Cauchy problemLie groupmethod of linesnonlinear diffusion equationmoving meshinvariant mesh

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) 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)

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Uses Software

• DASSL

Cites Work

• Similarity methods for differential equations
• Moving mesh methods based on moving mesh partial differential equations
• The asymptotic behaviour of the solution of the filtration equation
• Moving Mesh Partial Differential Equations (MMPDES) Based on the Equidistribution Principle
• FINITE DIFFERENCE MODELS ENTIRELY INHERITING CONTINUOUS SYMMETRY OF ORIGINAL DIFFERENTIAL EQUATIONS
• Self-similar behaviour for the equation of fast nonlinear diffusion
• Moving Mesh Methods for Problems with Blow-Up
• Symmetry-based algorithms to relate partial differential equations: I. Local symmetries
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