Wavelet-like collocation method for finite-dimensional reduction of distributed systems

被引:10
作者
Adrover, A
Continillo, G
Crescitelli, S
Giona, M
Russo, L
机构
[1] Univ Roma La Sapienza, Fac Ingn, Dipartimento Ingn Chim, I-00184 Rome, Italy
[2] Univ Sannio, Fac Ingn, I-82100 Benevento, Italy
[3] Univ Naples Federico II, Dipartimento Ingn Chim, I-80125 Naples, Italy
关键词
nonlinear dynamics; chaos; simulation; modal reduction;
D O I
10.1016/S0098-1354(00)00621-9
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
A wavelet-like collocation method is proposed to approach the reduction of dissipative distributed systems, expressed by means of partial differential equations, applying the methods of inertial manifold theory. The collocation method proposed, based on localized trial functions, provides a convenient numerical framework to develop approximate inertial manifolds in the case of partial differential problems (e.g. reaction/diffusion models) containing nonpolynomial nonlinearities. The collocation method is based on the interpolation of concentration/temperature fields by means of Gaussian-sine functions. As model systems, we consider reaction diffusion schemes such as the non-isothermal model for stockpile ignition and the Elezgaray-Ameodo diffusion model. (C) 2000 Elsevier Science Ltd. All rights reserved.
引用
收藏
页码:2687 / 2703
页数:17
相关论文
共 48 条
[31]  
Press W.H., 1994, NUMERICAL RECIPES
[32]   CONTROLLING SPATIOTEMPORAL PATTERNS ON A CATALYTIC WAFER [J].
QIN, F ;
WOLF, EE ;
CHANG, HC .
PHYSICAL REVIEW LETTERS, 1994, 72 (10) :1459-1462
[33]   FINITE-DIMENSIONAL BEHAVIOR IN DISSIPATIVE PARTIAL-DIFFERENTIAL EQUATIONS [J].
ROBINSON, JC .
CHAOS, 1995, 5 (01) :330-345
[34]   Arbitrarily accurate approximate inertial manifolds of fixed dimension [J].
Robinson, JC .
PHYSICS LETTERS A, 1997, 230 (5-6) :301-304
[35]   A CONCISE PROOF OF THE GEOMETRIC CONSTRUCTION OF INERTIAL MANIFOLDS [J].
ROBINSON, JC .
PHYSICS LETTERS A, 1995, 200 (06) :415-417
[36]   Nonlinear Galerkin methods for 3D magnetohydrodynamic equations [J].
Schmidtmann, O ;
Feudel, F ;
Seehafer, N .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1997, 7 (07) :1497-1507
[37]   INERTIAL MANIFOLDS - THE NONSELF-ADJOINT CASE [J].
SELL, GR ;
YOU, YC .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1992, 96 (02) :203-255
[38]   NONLINEAR GALERKIN METHOD USING CHEBYSHEV AND LEGENDRE POLYNOMIALS .1. THE ONE-DIMENSIONAL CASE [J].
SHEN, J ;
TEMAN, R .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1995, 32 (01) :215-234
[39]   CHAOTIC DYNAMICS OF COHERENT STRUCTURES [J].
SIROVICH, L .
PHYSICA D, 1989, 37 (1-3) :126-145
[40]   OPTIMAL LOW-DIMENSIONAL DYNAMIC APPROXIMATIONS [J].
SIROVICH, L ;
KNIGHT, BW ;
RODRIGUEZ, JD .
QUARTERLY OF APPLIED MATHEMATICS, 1990, 48 (03) :535-548