zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Adaptive interval wavelet precise integration method for partial differential equations. (English) Zbl 1144.65325
Summary: The quasi-Shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ordinary differential equations (ODEs). And then, an adaptive interval wavelet precise integration method (AIWPIM) for nonlinear partial differential equations (PDEs) is proposed. The numerical results show that the computational precision of AIWPIM is higher than that of the method constructed by combining the wavelet and the 4th Runge-Kutta method, and the computational amounts of these two methods are almost equal. For convenience, the Burgers equation is taken as an example in introducing this method, which is also valid for more general cases.
MSC:
65T60Wavelets (numerical methods)
65L05Initial value problems for ODE (numerical methods)
35F30Boundary value problems for first order nonlinear PDE
References:
[1]Zhong Wanxie. Precise computation for transient analysis[J].Computational Structural Mechanics and Applications, 1995,12(1):1–6 (in Chinese).
[2]Wei G W. Quasi wavelets and quasi interpolating wavelets[J].Chemical Physics Letters, 1998,296 (6):215–222. · doi:10.1016/S0009-2614(98)01061-6
[3]Silvia Bertoluzza. Adaptive wavelet collocation method for the solution of burgers equation[J].Transport Theory and Statistical Physics, 1996,25(3/5):339–352. · Zbl 0868.65071 · doi:10.1080/00411459608220705
[4]Wan Decheng, Wei Guowei. The study of quasi wavelets based numerical method applied to Burgers equations[J].Applied Mathematics and Mechanics (English Edition), 2000,21(10):1099–1110. · Zbl 1003.76070 · doi:10.1007/BF02458986
[5]Yan Guangwu. Study of Burgers equation using a lattice Bolizmann method[J].Acta Mechanica Sinica, 1999,31(2):143–151 (in Chinese).
[6]Zhang Xunan, Jiang Jiesheng. On precise time-integration method for nonlinear dynamics equations [J].Chinese Journal of Applied Mechanics, 2000,17(4):164–168 (in Chinese).