Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The BLUES function method applied to partial differential equations and
  analytic approximants for interface growth under shear   An iteration sequence based on the BLUES (beyond linear use of equation
superposition) function method is presented for calculating analytic
approximants to solutions of nonlinear partial differential equations. This
extends previous work using this method for nonlinear ordinary differential
equations with an external source term. Now, the initial condition plays the
role of the source. The method is tested on three examples: a
reaction-diffusion-convection equation, the porous medium equation with growth
or decay, and the nonlinear Black-Scholes equation. A comparison is made with
three other methods: the Adomian decomposition method (ADM), the variational
iteration method (VIM), and the variational iteration method with Green
function (GVIM). As a physical application, a deterministic differential
equation is proposed for interface growth under shear, combining Burgers and
Kardar- Parisi-Zhang nonlinearities. Thermal noise is neglected. This model is
studied with Gaussian and space-periodic initial conditions. A detailed Fourier
analysis is performed and the analytic coefficients are compared with those of
ADM, VIM, GVIM, and standard perturbation theory. The BLUES method turns out to
be a worthwhile alternative to the other methods. The advantages that it offers
ensue from the freedom of choosing judiciously the linear part, with associated
Green function, and the residual containing the nonlinear part of the
differential operator at hand.

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The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs