Polynomial particular solutions for certain partial differential operators.

*(English)*Zbl 1019.65096The 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.

Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca)

##### 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 |

##### Keywords:

nonhomogeneous linear elliptic and parabolic partial differential equations; method of fundamental solutions; numerical experiments; particular solutions; homogeneous boundary value problems; boundary-type methods
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\textit{M. A. Golberg} et al., Numer. Methods Partial Differ. Equations 19, No. 1, 112--133 (2003; Zbl 1019.65096)

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