Support-operators method for PDE discretization: symbolic algorithms and realization

The paper deals with the development and implementation of symbolic algorithms for the support-operators method for construction of finite-difference schemes. i.e., discretization of partial differential equations (PDEs), on a nonorthogonal logically rectangular grid. The general description of the support-operators method in the framework of the symbolic manipulation approach is presented. On the base of fundamental algorithms, developed earlier, algorithms for the construction of an adjoint difference operator are designed. These algorithms play a key role in the realization of the support-operators method. The algorithms have been implemented in the computer algebra system REDUCE. A 2D example demonstrates the power of the developed symbolic computation tool.