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Polynomial particular solutions for certain partial differential operators. (English) Zbl 1019.65096
The authors pay a lot of attention to the closed form of some particular solutions of some non-homogeneous linear elliptic and parabolic partial differential equations. With these particular solutions, they convert the equations into homogeneous ones. Consequently, the homogeneous boundary value problems are amenable to solution by boundary-type methods, particularly by the method of fundamental solutions. In the lack of any proofs, some numerical experiments are carried out in order to underline the efficiency of the approach.

MSC:
65N38 Boundary element methods for boundary value problems involving PDEs
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35K05 Heat equation
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