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Two approaches to the calculation of approximate symmetry exemplified using a system of advection-diffusion equations

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Ron WiltshireAuthors Info & Claims

Journal of Computational and Applied Mathematics, Volume 197, Issue 2

Pages 287 - 301

https://doi.org/10.1016/j.cam.2005.11.003

Published: 15 December 2006 Publication History

Abstract

Two algorithms used to evaluate the approximate symmetries of nonlinear systems are compared from a theoretical view point. The two quite distinct algorithms are cast into a form where one method can clearly be seen to be more general than the second. The circumstances for the equivalence of the two methods are presented and for these cases it is shown how the approximate symmetries found by one method may easily be calculated for the second. These ideas are exemplified by calculating new approximate symmetry reductions for a systems of advection-diffusion equations that describe the simultaneous transport of heat, moisture and solute in porous media and which contain unknown shape functions.

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Cited By

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Gorgone MOliveri F(2021)Consistent approximate Q-conditional symmetries of PDEs: application to a hyperbolic reaction-diffusion-convection equationZeitschrift für Angewandte Mathematik und Physik (ZAMP)10.1007/s00033-021-01554-272:3Online publication date: 13-May-2021
https://dl.acm.org/doi/10.1007/s00033-021-01554-2
Zhang ZChaolu T(2013)Homotopy series solutions of perturbed PDEs via approximate symmetry methodApplied Mathematics and Computation10.1016/j.amc.2013.09.028225(92-101)Online publication date: 1-Dec-2013
https://dl.acm.org/doi/10.1016/j.amc.2013.09.028

Index Terms

Two approaches to the calculation of approximate symmetry exemplified using a system of advection-diffusion equations
1. Mathematics of computing
  1. Mathematical analysis
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis

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cover image Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics Volume 197, Issue 2

15 December 2006

325 pages

ISSN:0377-0427

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Elsevier Science Publishers B. V.

Netherlands

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Published: 15 December 2006

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Gorgone MOliveri F(2021)Consistent approximate Q-conditional symmetries of PDEs: application to a hyperbolic reaction-diffusion-convection equationZeitschrift für Angewandte Mathematik und Physik (ZAMP)10.1007/s00033-021-01554-272:3Online publication date: 13-May-2021
https://dl.acm.org/doi/10.1007/s00033-021-01554-2
Zhang ZChaolu T(2013)Homotopy series solutions of perturbed PDEs via approximate symmetry methodApplied Mathematics and Computation10.1016/j.amc.2013.09.028225(92-101)Online publication date: 1-Dec-2013
https://dl.acm.org/doi/10.1016/j.amc.2013.09.028

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Advection-Diffusion-Reaction Equations: Hyperbolization and High-Order ADER Discretizations

Three-point combined compact difference schemes for time-fractional advection-diffusion equations with smooth solutions

An explicit high order method for fractional advection diffusion equations

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