Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Posteriori Error Bounds for Two Point Boundary Value Problems: A
  Green's Function Approach   We present a computer assisted method for generating existence proofs and a
posteriori error bounds for solutions to two point boundary value problems
(BVPs). All truncation errors are accounted for and, if combined with interval
arithmetic to bound the rounding errors, the computer generated results are
mathematically rigorous. The method is formulated for $n$-dimensional systems
and does not require any special form for the vector field of the differential
equation. It utilizes a numerically generated approximation to the BVP
fundamental solution and Green's function and thus can be applied to stable
BVPs whose initial value problem is unstable. The utility of the method is
demonstrated on a pair of singularly perturbed model BVPs and by using it to
rigorously show the existence of a periodic orbit in the Lorenz system.

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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio