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TitleAlgebraic construction of exact difference equations from symmetry of equations.
Author(s) Toshiaki Itoh
TypeBook, Chapter in Book, Conference Proceeding
AbstractDifference equations or exact numerical integrations, which have general solutions, are treated algebraically. Eliminating the symmetries of the equation, we can construct difference equations (DCE) or numerical integrations equivalent to some ODEs or PDEs that means both have the same solution functions. When arbitrary functions are given, whether we can construct numerical integrations that have solution functions equal to given function or not are treated in this work. Nowadays, Lie’s symmetries solver for ODE and PDE has been implemented in many symbolic software. Using this solver we can construct algebraic DCEs or numerical integrations which are correspond to some ODEs or PDEs. In this work, we treated exact correspondence between ODE or PDE and DCE or numerical integration with Gröbner base and Janet base from the view of Lie’s symmetries.
ISBN978-0-7354-0705-3/hbk; 978-0-7
URL http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.3241440
PublisherMelville, NY: American Institute of Physics (AIP)
Translation No
Refereed No