Structure-Preserving Numerical Methods for Differential Equations(Survey,<Special Topics>Activity Group "Scientific Computation and Numerical Analysis")

Abstract

"Structure-preserving numerical methods" for differential equations are such special methods that preserve certain structures in differential equations. Since the concept had been raised in 1980's for ordinary differential equations, the subject has been extensively studied, and now the related studies have spreaded also to partial differential equations. In this survey, the elements of such methods are outlined, and some recent progresses are briefly described.