ASP: automated symbolic computation of approximate symmetries of differential equations

DOI10.1016/j.cpc.2012.11.012zbMath1306.65267OpenAlexW2074436880MaRDI QIDQ483879

G. F. Jefferson, John Carminati

Publication date: 17 December 2014

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2012.11.012

zbMATH Keywords

symbolic computationapproximate symmetrysymmetries of differential equationsLie point symmetriesclassical symmetrycomputer package

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Second-order nonlinear hyperbolic equations (35L70) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Packaged methods for numerical algorithms (65Y15) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items (12)

On the numerical solutions of coupled nonlinear time-fractional reaction-diffusion equations ⋮ FracSym: automated symbolic computation of Lie symmetries of fractional differential equations ⋮ A consistent approach to approximate Lie symmetries of differential equations ⋮ Invariant solutions for a class of perturbed nonlinear wave equations ⋮ \(n^{\text{th}}\)-order approximate Lagrangians induced by perturbative geometries ⋮ Explicit invariant solutions associated with nonlinear atmospheric flows in a thin rotating spherical shell with and without west-to-east jets perturbations ⋮ Nonlinear Analysis of Perturbed Rotating Whirlpools in the Ocean and Atmosphere ⋮ Analytical and numerical solutions of time and space fractional advection-diffusion-reaction equation ⋮ Numerical solutions of space-fractional advection-diffusion equations with nonlinear source term ⋮ On the second-order approximate symmetry classification and optimal systems of subalgebras for a forced Korteweg-de Vries equation ⋮ Exact and numerical solutions of time-fractional advection-diffusion equation with a nonlinear source term by means of the Lie symmetries ⋮ Lie symmetry analysis and exact solutions of generalized fractional Zakharov-Kuznetsov equations

Uses Software

• GeM
• Maple
• SYMMGRP
• DESOLVII
• DESOLV
• ASP

Cites Work

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• Comparison of approximate symmetry methods for differential equations
• A comparative study of some computer algebra packages which determine the Lie point symmetries of differential equations
• Similarity solutions of partial differential equations using DESOLV
• GeM software package for computation of symmetries and conservation laws of differential equations
• Approximate and renormgroup symmetries
• Review of symbolic software for Lie symmetry analysis
• An approximate Lie group investigation into the spreading of a liquid drop on a slowly dropping flat plane
• Finding higher symmetries of differential equations using the MAPLE package DESOLVII
• Symbolic computation and differential equations: Lie symmetries
• Two approaches to the calculation of approximate symmetry exemplified using a system of advection-diffusion equations
• On approximate symmetry and approximate solutions of the nonlinear wave equation with a small parameter
• APPROXIMATE SYMMETRIES
• CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
• Symmetries and differential equations

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