Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation of Stochastic Partial Differential Equations by a
  Kernel-based Collocation Method   In this paper we present the theoretical framework needed to justify the use
of a kernel-based collocation method (meshfree approximation method) to
estimate the solution of high-dimensional stochastic partial differential
equations (SPDEs). Using an implicit time stepping scheme, we transform
stochastic parabolic equations into stochastic elliptic equations. Our main
attention is concentrated on the numerical solution of the elliptic equations
at each time step. The estimator of the solution of the elliptic equations is
given as a linear combination of reproducing kernels derived from the
differential and boundary operators of the SPDE centered at collocation points
to be chosen by the user. The random expansion coefficients are computed by
solving a random system of linear equations. Numerical experiments demonstrate
the feasibility of the method.

18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: stat