Editing Partial differential equation (section)

===Semi-analytical methods===
The [[Adomian decomposition method]],<ref>{{cite book |title=Solving Frontier problems of Physics: The decomposition method |first=G. |last=Adomian|author-link=George Adomian|publisher=Kluwer Academic Publishers |year=1994 |isbn=9789401582896 |url=https://books.google.com/books?id=UKPqCAAAQBAJ&q=%22partial+differential%22}}</ref> the [[Aleksandr Lyapunov|Lyapunov]] artificial small parameter method, and his [[homotopy perturbation method]] are all special cases of the more general [[homotopy analysis method]].<ref>{{cite book | last=Liao | first=S. J. |author-link=Liao Shijun| title=Beyond Perturbation: Introduction to the Homotopy Analysis Method | publisher=Chapman & Hall/ CRC Press | location=Boca Raton | year=2003 | isbn=1-58488-407-X }}</ref> These are series expansion methods, and except for the Lyapunov method, are independent of small physical parameters as compared to the well known [[perturbation theory]], thus giving these methods greater flexibility and solution generality.