Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A high-precision method for general nonlinear initial-boundary value
  problems   A high precision, and space time fully decoupled, wavelet formulation
numerical method is developed for a class of nonlinear initial boundary value
problems. This method is established based on a proposed Coiflet based
approximation scheme with an adjustable high order for a square integrable
function over a bounded interval, which allows expansion coefficients to be
explicitly expressed by function values at a series of single points. In
applying the solution method, the nonlinear initial boundary value problems are
first spatially discretized into a nonlinear initial value problem by combining
the proposed wavelet approximation scheme and the conventional Galerkin method.
A novel high order step by step time integrating approach is then developed for
the resulting nonlinear initial value problem using the same function
approximation scheme based on wavelet theory. The solution method is shown to
have Nth-order accuracy, as long as the Coiflet with [0, 3N-1] compact support
is adopted, where N can be any positive even number. In addition, the stability
property of the method is analyzed, and the stable domain is determined.
Numerical examples are considered to justify both the accuracy and efficiency
of the method. Results show that the proposed solution method has better
accuracy and efficiency than most other methods.

23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat