Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regular polynomial interpolation and approximation of global solutions
  of linear partial differential equations   We consider regular polynomial interpolation algorithms on recursively
defined sets of interpolation points which approximate global solutions of
arbitrary well-posed systems of linear partial differential equations.
  Convergence of the 'limit' of the recursively constructed family of
polynomials to the solution and error estimates are obtained from a priori
estimates for some standard classes of linear partial differential equations,
i.e. elliptic and hyperbolic equations. Another variation of the algorithm
allows to construct polynomial interpolations which preserve systems of linear
partial differential equations at the interpolation points. We show how this
can be applied in order to compute higher order terms of WKB-approximations of
fundamental solutions of a large class of linear parabolic equations. The error
estimates are sensitive to the regularity of the solution. Our method is
compatible with recent developments for solution of higher dimensional partial
differential equations, i.e. (adaptive) sparse grids, and weighted Monte-Carlo,
and has obvious applications to mathematical finance and physics.

1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
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The categories of this paper are: nlin
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci