Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polar differentiation matrices for the Laplace equation in the disk
  subjected to nonhomogeneous Dirichlet, Neumann and Robin boundary conditions
  and the biharmonic equation subjected to nonhomogeneous Dirichlet conditions   In this paper we present a pseudospectral method in the disk. Unlike the
methods known until now, the disk is not duplicated. Moreover, we solve the
Laplace equation subjected to nonhomogeneous Dirichlet, Neumann and Robin
boundary conditions and the biharmonic equation subjected to nonhomogeneous
Dirichlet conditions by only using the elements of the corresponding
differentiation matrices. It is worth noting that we don not use any
quadrature, do not need to solve any decoupled system of ordinary differential
equations, do not use any pole condition and do not require any lifting. We
solve several numerical examples showing that the spectral convergence is being
met. The pseudospectral method developed in this paper can be applied to
estimate Sherwood numbers integrating the mass flux to the disk and it can be
easily implemented to solve Lotka-Volterra systems and nonlinear problems
involving chemical reactions.

8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas