Solvability of partial differential equations by meshless kernel methods. (English) Zbl 1136.65111
Summary: This paper first provides a common framework for partial differential equation problems in both strong and weak form by rewriting them as generalized interpolation problems. Then it is proven that any well-posed linear problem in strong or weak form can be solved by certain meshless kernel methods to any prescribed accuracy.
MSC:
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
References:
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