Commun. Comput. Phys., 6 (2009), pp. 109-130.

Wavelet Galerkin Methods for Aerosol Dynamic Equations in Atmospheric Environment

Dong Liang 1*, Qiang Guo 1, Sunling Gong 2

1 Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada.
2 Air Quality Research Division, S & T Branch, Environment Canada, 4905 Dufferin Street, Toronto, Ontario, M3H 5T4, Canada.

Received 14 January 2008; Accepted (in revised version) 10 September 2008
Available online 18 November 2008


Aerosol modelling is very important to study and simulate the behavior of aerosol dynamics in atmospheric environment. In this paper, we consider the general nonlinear aerosol dynamic equations which describe the evolution of the aerosol distribution. Continuous time and discrete time wavelet Galerkin methods are proposed for solving this problem. By using the Schauder's fixed point theorem and the variational technique, the global existence and uniqueness of solution of continuous time wavelet numerical methods are established for the nonlinear aerosol dynamics with sufficiently smooth initial conditions. Optimal error estimates are obtained for both continuous and discrete time wavelet Galerkin schemes. Numerical examples are given to show the efficiency of the wavelet technique.

AMS subject classifications: 52B10, 65D18, 68U05, 68U07

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Key words: Aerosol dynamics, wavelet Galerkin methods, semi-discrete, fully-discrete, existence, error estimate.

*Corresponding author.
Email: (D. Liang), (Q. Guo), (S. Gong)

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