Abstract
Abstract This paper presents techniques for the mathematical modeling of physical systems which are described by linear and non-linear partial differential equations. The most popular numerical methods for the solution of non- linear and even some linear problems are based on finite-difference approximations for the derivatives. This paper presents finite-difference methods which are most suitable when changes are taking place in all three space coordinate directions and in the time direction. The main concern here is with physical systems – such as petroleum reservoirs – which are often described by a set of parabolic and/or elliptic partial differential equations.
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