Open AccessThe approximate homotopy symmetry reduction for far-field model equation
Author(s) -
Xiaoyu Jiang
Publication year - 2011
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.60.120201
Subject(s) - homotopy analysis method , homotopy , reduction (mathematics) , similarity (geometry) , mathematics , ordinary differential equation , dimensional reduction , series (stratigraphy) , n connected , symmetry (geometry) , mathematical analysis , field (mathematics) , differential equation , convergence (economics) , pure mathematics , mathematical physics , computer science , geometry , paleontology , artificial intelligence , biology , economic growth , economics , image (mathematics)
The far-field model equation is investigated by the approximate homotopy symmetry method. Homotopy series solutions are constructed through summarizing the relevant general formulas for similarity reduction solutions and similarity reduction equations of differernt orders. Similarity reduction equations of different orders are linear variable coefficients ordinary differential equations, and can be solved one by one from zero-order similarity reduction equations. The auxiliary parameter in the homotopy model affects convergence of homotopy series solutions.