A Heat Transfer with a Source: the Complete Set of Invariant Difference Schemes

DOI10.2991/jnmp.2003.10.1.3zbMath1026.65072arXivmath/0309139OpenAlexW3099145424MaRDI QIDQ4805768

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Publication date: 16 December 2003

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0309139

zbMATH Keywords

Lie group symmetriesheat transfer equationsinvariant differenceequations

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) General properties and structure of real Lie groups (22E15) Lattice dynamics; integrable lattice equations (37K60)

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One-Dimensional Flows of a Polytropic Gas: Lie Group Classification, Conservation Laws, Invariant and Conservative Difference Schemes ⋮ Convecting reference frames and invariant numerical models ⋮ Conservative invariant finite‐difference schemes for the modified shallow water equations in Lagrangian coordinates ⋮ Comparison of some Lie-symmetry-based integrators ⋮ One-dimensional gas dynamics equations of a polytropic gas in Lagrangian coordinates: symmetry classification, conservation laws, difference schemes ⋮ Shallow water equations in Lagrangian coordinates: symmetries, conservation laws and its preservation in difference models ⋮ Conformally invariant elliptic Liouville equation and its symmetry-preserving discretization ⋮ Invariant conservation law-preserving discretizations of linear and nonlinear wave equations ⋮ Exponential splitting time integration for pseudospectral methods on moving meshes ⋮ The discretized Boussinesq equation and its conditional symmetry reduction

Cites Work

• Transformation groups in network spaces
• An invariant moving mesh scheme for the nonlinear diffusion equation
• Lie point symmetry preserving discretizations for variable coefficient Korteweg-de Vries equations
• Lie group classification of second-order ordinary difference equations
• Symmetry-adapted moving mesh schemes for the nonlinear Schrödinger equation
• Symmetries and Integrability of Difference Equations
• Symmetry-preserving difference schemes for some heat transfer equations
• Lie symmetries of multidimensional difference equations
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