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Solving PDEs

In [59] the standard form of a system of PDEs is used to construct a directed graph, which is then used as the basis for an algorithm for the integration of the system.

In [63] the standard form of a system of linear PDEs is used as the basis of an algorithm to recursively solve systems of linear PDEs in their coefficient field by decoupling and solving ``ODEs''. As an application of this algorithm we show that: If the solution space of a system of linear PDEs is finite-dimensional and the coefficients of the system are all rational functions of the system's independent variables, then all rational function solutions of the system can be determined.



Greg Reid 2003-11-24